Masarykova univerzita
Filozofická fakulta
Mojmír Dočekal
Czech Negation from the Formal
Perspective
BRNO
2015
Reviewers of the book: Prof. RNDr. Jaroslav Peregrin, CSc. (Academy of Sciences ČR)
doc. PhDr. Ludmila Veselovská, Ph.D. (Palacký University, Olomouc)
Prof. Dr. Hedde Zeijlstra (University of Göttingen)
The work on this book was supported by the GAČR (grant no 405/07/P252) and by
the Faculty of arts MU (grant no ROZV/20/FF/DOC/2015).
To the memory of my parents
Contents
Introduction vii
1 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
3 List of frequently used symbols . . . . . . . . . . . . . . . . . . . . . . . x
1 The Frameworks 1
1.1 NPs as generalized quantifiers . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 NPs as sets of sets . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Classification of determiners in the generalized quantifiers framework 5
1.1.3 Monotonicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Formal framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Language of plurality . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Maximalization of different NPs . . . . . . . . . . . . . . . . . . . 12
1.2.3 Scopal and non-scopal NPs . . . . . . . . . . . . . . . . . . . . . . 15
1.2.3.1 Cumulativity, collectivity and distributivity . . . . . . . 16
1.2.4 Negation in LoP . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2.4.1 Verbal negation . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.5 Quantifiers and negation . . . . . . . . . . . . . . . . . . . . . . . 21
1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 The Language of Events and Plurality . . . . . . . . . . . . . . . 23
1.4.2 Syntax of the Language of Events and Plurality . . . . . . . . . . 23
1.4.3 Semantics of the Language of Events and Plurality . . . . . . . . 25
2 The nature of negative noun phrases 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 The puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Type shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Two Theories of Type Shifting between Arguments and Predicates . . . 33
2.4.1 Partee’s Type Shifting Triangle . . . . . . . . . . . . . . . . . . . 33
2.4.2 The Adjectival Theory of Indefinites . . . . . . . . . . . . . . . . 35
2.4.3 Partee’s pragmatic restriction on type shifting . . . . . . . . . . . 36
2.5 Linking Syntax and Semantics of Type Shifting . . . . . . . . . . . . . . 37
2.5.1 Choice functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.5.2 Czech n-words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Prediction I: predicative positions . . . . . . . . . . . . . . . . . . . . . 42
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2.7 Prediction II: collectivity . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.7.1 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.7.2 Coordination of n-words . . . . . . . . . . . . . . . . . . . . . . . 48
2.7.3 Negative NPs in Czech and English and their formalization in LoP 49
2.7.3.1 English negative NPs in LoP . . . . . . . . . . . . . . . 51
2.7.3.2 Czech negative NPs in LoP . . . . . . . . . . . . . . . . 53
2.8 Prediction III: intensional predicates . . . . . . . . . . . . . . . . . . . . 54
2.9 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Negation and aspect 59
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Time and aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.1 Modification of time intervals . . . . . . . . . . . . . . . . . . . . 62
3.2.1.1 Event time modification . . . . . . . . . . . . . . . . . . 62
3.2.1.2 Utterance time modification . . . . . . . . . . . . . . . . 62
3.2.1.3 Reference time modification . . . . . . . . . . . . . . . . 62
3.2.2 Negation and time modification . . . . . . . . . . . . . . . . . . . 63
3.2.3 Downward entailing predicates . . . . . . . . . . . . . . . . . . . . 65
3.3 Dokud and until . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 The one until vs. two until approaches . . . . . . . . . . . . . . . . . . . 74
3.5 Dokud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6 Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.6.1 Dokud in embedded atelic sentences . . . . . . . . . . . . . . . . . 79
3.6.2 Dokud in embedded telic sentences . . . . . . . . . . . . . . . . . 82
3.7 Dokud and negative concord . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 Negation and the scope of quantifiers 88
4.1 Data from the corpus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.1 SV linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.2 VS linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 Events and partitives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Why ¬ > ∀? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4.1 *O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5 ∀ > ¬ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.5.1 Independent evidence for the presupposition of homogeneity . . . 104
4.6 Information structure and the scope of operators . . . . . . . . . . . . . . 106
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 On negative manner and degree questions 109
5.1 The data – landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.1.1 Tenseless wh-questions . . . . . . . . . . . . . . . . . . . . . . . . 110
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5.1.2 VP-adverbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.1.3 Negatives and other affective operators . . . . . . . . . . . . . . . 112
5.1.4 Presuppositional islands . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.5 Extraposition islands . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.6 Comparative islands . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.1.7 Interim summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2 The data – zooming into negative manner and degree questions . . . . . 114
5.3 Intervention effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.3.1 Consequences of the reduction of weak islands to the intervention
effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.4 Aspect and weak islands . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.4.1 Semantics of questions . . . . . . . . . . . . . . . . . . . . . . . . 124
5.4.2 Exhaustivity and negative degree and manner questions . . . . . . 127
5.4.3 Perfective aspect as an exhaustive marker . . . . . . . . . . . . . 128
5.4.3.1 Non-exhaustive operator answer3 . . . . . . . . . . . . . 128
5.4.3.2 Telicity and exhaustivity . . . . . . . . . . . . . . . . . . 129
5.4.3.3 Perfective aspect forces exhaustivity . . . . . . . . . . . 133
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Summary 138
Bibliography 139
vi
Introduction
1 Acknowledgments
I am very grateful to my dear colleagues and students who read or heard large portions
of this book and provided me with so much needed comments and feedback. I especially
want to thank to the three reviewers of my book (in the alphabetical order): Jaroslav
Peregrin, Lída Veselovská and Hedde Zeijlstra. Thanks to their comments and suggestions
the book looks better and hopefully reads a bit easier too. Ivona Kučerová helped
me to shape many ideas which appear scattered through the book, so big thanks to
her across the ocean. My greatest intellectual debt is undoubtedly in Fred Landman’s
work, as I use his Language of Events and Plurality in every chapter of this book. I
hope I didn’t simplified his theories too much and I am very grateful to him for his
kind explanation of more difficult parts of his framework to me. I also want to thank
members of the Department of Linguistics and Baltic languages for providing me with a
great working place, particularly I am grateful to Ondřej Šefčík for being the best boss
which I ever had (honestly) and Václav Blažek for kindly reminding me that I should
finish the book better sooner than later; finally all the others member of our department
for making Brno a good place for the intellectual work.
Next I want to warmly thank all those students who attended my lectures in Brno
for participating in them and for their comments and discussions. I am also grateful to
the participants of various conferences where I have given presentations of parts of the
material in this book.
In addition to the people I already mentioned I am especially grateful to all friends,
linguists, logicians and students which I happily met at various places on Earth, these
include Jitka Bartošová, Daniel Büring, Pavel Caha, Jenny Doetjes, Jakub Dotlačil,
Joseph Emonds, Berit Gehrke, Eva Hajičová, Romana Holomčíková, Dalina Kallulli,
Petr Karlík, Lanko Marušič, Louise McNally, Hana Strachoňová, Barbara Tomaszewicz,
Lída Veselovská, Michael Wagner, Marcin Wągiel, Henk Zeevat, Markéta Ziková, Rok
Žaucer and many others.
Some ideas in this book are based on earlier versions of my attempts to describe the
formal properties of Czech negation. A previous version of chapter 3 was published
as Dočekal (2011). Some of the ideas of chapter 4 appeared in Dočekal (2012b). The
material presented in chapter 6 is a part of a joint work with Ivona Kučerová and is to
some extent contained in our article Dočekal and Kučerová (2013). However, much of
the text in these articles was rewritten and a lot of material was added. And the present
book improves upon the analyses reported in the articles in many respects.
The last three years in which I worked on this book were filled with major changes in
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Introduction
my life. I became the father of my lovely twins, Mariana and Mojmír and even though
I haven’t looked like that all the time, I certainly know that nothing in Czech negation
is more important than their screaming ne ne ne ne, tati. I also want to express very
special thanks to my wife Markéta, because without her support I wouldn’t have written
a single word of this book.
2 Introduction
This book deals with the meaning of Czech negation. The general framework is formal
semantics, a model-theoretic style of explaining the meanings of natural language
through the reference of its expressions. I build on the nowadays well established tradition
which started 40 years ago with Montague (1973). I focus a lot on the formal
analyses of negation (as already suggested by the title of the book), which necessarily
means that some (very interesting) aspects of natural language negation lie beyond the
grasp of my theories. This is the main reason I mostly just touch the issues which are
concerned with the pragmatics of negation and which were of the central interest to
Czech linguists dealing with negation (such as Hajičová (1973), Hajičová (1974) and
Petr et al. (1986)).
In Chapter 1, I introduce the semantic theory developed in Landman (2000) and Landman
(2004). Landman’s Language of Events and Plurality will be the main framework I
will use in the rest of the book as it offers very restrictive and heuristically extraordinarily
useful formalization of natural language negation.
In chapter 2, I will be concerned with the formalization of the meaning of negative
noun phrases in Czech. I will aim to establish their indefinite status and compare
them with regular quantifiers which can be found in non-negative concord languages like
English.
In Chapter 3, I will be concerned with the interaction between negation and lexical
aspect. As negation seems to behave in some cases as a lexical aspect operator which is
able to turn telic events into atelic ones. Regarding that issue, I will claim that the proper
understanding of the natural language aspect allows us to retain the simple semantics
for negation as the truth-reversing function and that natural language negation doesn’t
have any special aspectual properties.
In Chapter 4, I will be concerned with the scope preferences of negation in sentences
with universal subjects. I will claim that the most decisive factor is the concurrence in
natural language and that for most cases this concurrence results in the fixation of scope
between the negation and the universal quantifier.
In Chapter 5, I will be concerned with two types of negative questions – negative degree
and negative manner questions. Such questions were reported in some languages as
ungrammatical which was theoretically explained as them being weak islands – schematically
configurations from which wh-movement isn’t possible. Czech negative manner and
degree questions are grammatical though which I take as an empirical argument against
the current theories of weak islands. An attempt to reduce the cross-linguistic variation
of the negative degree and manner questions to the exhaustivity and intervention effects
viii
Introduction
is accomplished in that chapter.
This book is not intended to play the role of the comprehensive guide to Czech negation
(or negation cross-linguistically – see Horn (1989) for the Book of that kind). The nature
of the tools I use and my own intellectual limits restrict my linguistic enterprise so that
it results in four case studies connected by the data and the method – Czech negation
and formal semantics respectively. Nevertheless, at least for me the case studies reveal
a nice and elegant grammar machine of Czech even if in small details. I can only hope
that this impression will be at least partially shared by the potential readers of the book.
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Introduction
3 List of frequently used symbols
Symbol Description
1 truth value True
0 truth value False
¬ negation
∧ conjunction
∨ disjunction
→ material implication
↔ equivalence
∀ universal quantifier
∃ existential quantifier
t, t , t , . . . variables over time
x, y, z, . . . variables over entities
e1, e2, . . . variables over events
α semantics of α
X ⊆ Y X is a subset or equals Y
P, Q, R, . . . variables over predicates
X, Y, Z, . . . variables over sets
∅ empty set
∩ set intersection
∪ set union
|X| cardinality of X
d type of entities
e type of events
t type of truth-values
α, β type of functions from α-entities to β-entities
∗
ungrammatical expression (especially in front of natural language expressions)
∗
pluralization (in front of Language of Pluralities expressions)
# semantical anomaly
Ag, Th, . . . thematic roles
↑ group formation
λx.α function from x into α
a b sum of a and b
x
1 The Frameworks
The main topic of this book is the natural language negation and its interaction with
various aspects of the grammar of natural language: the second chapter of the book
explores how the morphological negation on verb and on noun phrases is interpreted
in Czech (as a negative concord language) and English, in the third chapter I will
explore the interaction between negation and grammatical aspect, in the fourth chapter
I will look at various scope interactions between negation and different quantified and
numerical noun phrases, and in the last chapter I will examine the interpretation of some
types of negative questions.
But before I will go for the different topics I just mentioned, I will summarise two big
frameworks for the treatment of natural language semantics. First, in the section 1.1 I
will provide an introduction into the framework of generalized quantifiers, a framework
that has proven its great use for the study of natural language quantification in the past
three decades, see Barwise and Cooper (1981) for the classical reference.
Second, in the section 1.2 I will show the main ingredients of the Language of Events
and Plurality (LoP henceforth). LoP is based on the work of Landman (2000) and
Landman (2004) which on Landman’s previous work on the plurality in natural language,
as reported in Landman (1989) and Landman (1997). LoP is extensively used for the
description of plurality interpretation in the current formal semantics. But LoP offers
a very exciting perspective for treatment of negation in natural language, as it fixes the
scope of the verbal negation in the formalization over the existential closure of the event
variable as I will demonstrate in the section 1.2.
Second motivation for my usage of LoP is the simple fact that it represents one of
the rare exceptions in the modern formal semantics: it is a full blown framework with
formalization of many ideas which were treated just as intuitions before. And lastly, the
usage of LoP allowed me to understand many subtle issues of the plurality and aspect
interactions with negation which I think are not possible to handle in any alternative
framework I am aware of. But before I will introduce LoP, let me go through one historical
step – a summary of the main concepts of the Generalized Quantifiers framework,
which I think allows us to understand comparatively what is so important and beautiful
about LoP.
1.1 NPs as generalized quantifiers
The article by Barwise and Cooper (1981) can be considered a cornerstone in the field
of formal semantic treatment of noun phrases meaning. Barwise and Cooper (1981)
draw on Montague (1973) in building an unified semantics of any kind of NPs, be they
1
1 The Frameworks
as different as definites, indefinites, quantified noun phrases or noun phrases headed by
cardinals. We can interpret this style of theory as the followers of Montague’s idea that
one syntactic category should be always translated as the same semantic object. Even
if this unification can be required from the methodological point of view, its realisation
collides with some empirical data as we will see. But let’s put this aside and for now I
will provide a brief introduction into the framework of Generalized Quantifiers.
Barwise and Cooper (1981) start with two critical comments regarding the predicate
logic treatment of quantification in natural language. First, the syntactic structure of
quantified formulas in predicate logic and the syntactic structure of quantified sentences
in natural language are according to Barwise and Cooper unsatisfactorily different. As
an illustration, let’s look at the following examples with the predicate logic formalization.
The quantifiers every/some must be translated as “discontinuous” constituents made of
predicate logic operators ∀... → and ∃...∧ respectively. This of course renders the truth
conditions of the sentences right but goes a lot against the well established assumption
that there’s a correspondence between “constituent” structure of natural and formal
language. Which means that if we have one phrase in natural language, we would
expect that there’s one unit in the formal language which will correspond to it.
(1) a. Every student is lazy.
a’ ∀x[student(x) → lazy(x)]
b. Some students are lazy.
b’ ∃x[student(x) ∧ lazy(x)]
Second, Barwise and Cooper proved, that an NP such as most N isn’t expressible the
predicate logic of the first order. The natural language sentence like (2) cannot be
formalized in the first-order predicate logic, even if we enrich its vocabulary with a
third quantifier M corresponding to the natural language most. There are two possible
translations of most into predicate logic – (3-a) and (3-b) – parallel to the existential
and universal quantifiers as the formal logic translation of some and every.
(2) Most students are lazy.
(3) a. Mx[student(x) ∧ lazy(x)]
b. Mx[student(x) → lazy(x)]
Consider a situation in which there are 20 people, 5 of them are students. If 4 of these
students are lazy, sentence (2) is uncontroversially true. But the truth conditions of
(3-a) would output falsehood, as it’s not true that most of the individuals (20) in the
universe of discourse are both students and both lazy. In other words: the formalization
in (3-a) doesn’t render the truth conditions of the natural language sentence right.
But (3-b) doesn’t fare better – it would output true in a first scenario but in a different
scenario with 20 people, 5 students and only one of the students being lazy, (3-b) would
be true unlike its natural language counterpart. Why? Because implication returns
truth for any case where its antecedent is false, so 15 non-students would make the
whole formula true, regardless of the number of lazy individuals among the students.
Again a wrong result.
2
1 The Frameworks
The discussion above indicates some of the problems that are met when one tries to
define the first-order version of most. The main problem with the predicate-logic formalization
of natural language quantification is that predicate logic does allow unrestricted
quantification (e.g. predicate-logic formula ∀xP(y) is syntactically and semantically wellformed
in predicate logic) but every natural language quantifier comes with a restriction.
This restriction can be a bit sloppily emulated with the predicate-logic connectives in
case of the quantifiers like all/some/two/... but this strategy fails in the case of the
quantifier most e.g. I refer the diligent reader to Barwise and Cooper (1981) for further
details and for the formal proof of unusability of the first order logic for the treatment of
natural language quantifiers like most. This is one of the main reasons why Barwise and
Cooper introduce a more robust and more efficient framework – generalized quantifiers.
The main ideas of generalized quantifiers will be discussed in the next section.
1.1.1 NPs as sets of sets
The theory of generalized quantifiers brings a solution to both problems of predicate
logic mentioned in the previous section – it is able to formalize the meaning of any
natural language determiner (and moreover in a uniform fashion) and it assigns the
non-discontinuous meaning to the determiners, making the formal language closer to the
surface of the natural language. It achieves this goal by going beyond the boundaries of
the first order logic: the intuitive meaning of the generalized quantifiers formalization of
most in (4) is: most noun denotes the set of all properties which the most instantiations
of noun bear. In other words, a generalized quantifier like most sailors denotes such
set of properties which most sailors exemplify, e.g. the set of rum-drinkers, the set of
swimmers and the set of scary songs singing individuals would be some of the sets in
the set of sets denotation of the generalized quantifier most sailors (at least if we stick
to the conventional image of a sailor). (4) (I follow the set notation which can be found
in de Hoop (1992) e.g. as it seems to me more readable than the usual λ functional
notation of generalize quantifiers) formalizes just this: mostN denotes such set of sets
(X) over the universe of discourse (X ⊆ E) where each set member of X contains most
Ns. The logical type of a generalized quantifier reflects this: its type is the e, t , t , the
function from sets ( e, t ) to the truth values ( t ).
(4) Most N = {X ⊆ E : X contains most Ns}
(E stands for the domain of discourse)
Generalized quantifiers offer a natural unification for the denotation of all types of NPs
– the format is so rich that any type of NP meaning can be treated like a set of sets.
This goes pretty well with the old Montague’s impetus for the uniform mapping of the
syntactical categories to the semantic types. In the generalized quantifiers framework
all NPs are treated at the e, t , t type. This seems rather unintuitive at the first sight
at least for the proper names, which were at least since Frege’s (1892) seminal paper
treated like entities (hence of the e type). But in generalized quantifiers the proper
names can be represented as sets of properties which the respective entity instantiates.
3
1 The Frameworks
If we accept a well established rule which constraints the conjunction only to the
expressions of the same semantic type (and of course of the same syntactic category),
we must admit that a proper name like Peter in (5) is of the same type as the generalized
quantifier some students.
(5) I met Peter and some students.
Montague’s solution to the conjunction problem was following from his uniform treatment
of noun phrases semantics. As was already mentioned, it’s straightforward to
represent meaning of proper names as set of sets (type e, t , t ), namely the as the set
of all properties which the individual denoted by the proper name has. Then the logical
type of proper name and quantifier like some students in (5) match and conjunction can
apply. The Montague’s strategy, even though formally coherent, was the generalization
to the worst case: if some expression from natural language must be represented as a
higher type in some context, then the expression must be represented as the higher type
in all contexts. In that case, even the sentence Peter smokes is true if the set of smokers
is one of the sets in the set of sets of properties which Peter has; and the sentence isn’t
formalized as a member-set relation between individual Peter and set of smokers. It is
if course more natural to think about the denotation of a proper name like Peter as of
an individual of the type e then as of set of sets of his properties but that doesn’t
make any argument against the Montague’s theory; nevertheless we will see soon some
real empirical problems which generalized quantifiers theory (following Montague in this
respect) encounters. Partee and Rooth (1983) started a different tradition in dealing
with this phenomena but I will introduce their type-shifting framework later.
Let’s look at some examples of the generalized quantifiers treatment of the natural
language determiners. (6-a) represents the meaning of all – all N is such set of sets,
where each set contains all members of the N denotation ( N ⊆ X). (6-b) represents
the meaning of no: no N is such set of sets which don’t have any intersection with the
denotation of N ( N ∩ X = ∅). The generalized quantifier no sailors would denote set
of sets like set denotation of the following VPs: live on Mars, be a hamster, be a prime
number. The last example: numerical generalized quantifier in (6-c) denotes such set of
sets which has the n-numerous intersection with the denotation of the N – a generalized
quantifier like at least two presidents of the Czech Republic would represent a set of sets
with the members like {x ∈ E : x’s first name is Václav}, {x ∈ E : x wears glasses},
. . . The generalized quantifier denotations in (6) correspond to total functions.
(6) a. all N = {X ⊆ E : N ⊆ X}
b. no N = {X ⊆ E : N ∩ X = ∅}
c. at least n N = {X ⊆ E : | N ∩ X| ≥ n}
d. most N = {X ⊆ E : | N ∩ X| > | N − X|}
But the interpretation of some NPs in natural language is better treated as partial functions,
the prime example are definite NPs such as the N or both N. Their denotation is
given in (7): they are built on the semantics of generalized quantifier all but output undefined
truth-value if the cardinality of the noun denotation doesn’t meet the respective
4
1 The Frameworks
criterion. So NP like the president of the Czech Republic outputs undefined (unless the
domain of quantification is contextually restricted to the present president or whoever
else), because the Czech Republic had more than one representant of the role.
(7) a. the n N = all N iff | N | = n, otherwise undefined
b. both N = all N iff | N | = 2, otherwise undefined
Even if the generalized quantifiers framework works with sets of sets, there is a concept
of witness sets introduced by Barwise and Cooper to go down in order: from sets of
set to sets. Intuitively, we think about sentences like John is a sailor in terms of set
membership: the sentence is true if John is the member of the set of sailors (formally:
j ∈ {x | x is a sailor}). But Barwise and Cooper (1981), following Montague (1973),
argue exactly for the opposite perspective with respect to what is the function and what
is its argument: a sentence like John is a sailor is true in their framework if and only
if the property of being a sailor is one of the properties (family of sets) which John has
(formally: {x | x is a sailor} ∈ {X ⊆ E | j ⊆ X}). The idea of witnesses (or witness
sets) can be understood as restoring the former intuition: the witness set for John is a
singleton set {j}, and the sentence John is a sailor is true if and only if the witness set
for John is a subset of the set of sailors. Similarly for quantifiers: the witness set of the
quantifier every sailor is the set of sailors, the witness set of the quantifier two sailors is
the set of sets containing as members sets of two sailors and so on.
1.1.2 Classification of determiners in the generalized quantifiers
framework
The generalized quantifiers framework lead to many fruitful outcomes: one of them is the
search for formally meaningful semantic universals. The basic idea defended by Barwise
and Cooper is that natural language determiners are constrained to form just a subset
of logically possible relations between sets. In other words, no natural language contains
determiners which wouldn’t satisfy all basic constraints as Extension, Conservativity and
Quantity discussed in detail in Barwise and Cooper (1981) and sketched shortly below.
Because the issue of semantic universals is tangential to the purposes of my book, I will
just shortly mention two of the semantic universals: extension and conservativity.
The extension constraint is formalized in (8) and in a nutshell it says that enlarging
the universe of discourse (E ⊆ E ) shouldn’t change the truth value of the determiner
(DEAB ↔ DE AB). Consider a natural language sentence like (9). This sentence (if
true) in a universe of discourse containing just entities in the Czech Republic should
remain true even if we enlarge the universe of discourse to all European countries; this
holds of course only if the denotation of A (sailors) and B (smokers) is kept fixed as
stated in the formula (DEAB ↔ DE AB).
(8) Extension
A, B ⊆ E ⊆ E’ → (DEAB ↔ DE AB)
(9) All sailors smoke.
5
1 The Frameworks
Another universal of Barwise and Cooper is conservativity, as defined in (10), it says
that the truth-values of any determiner remain the same, if we substitute its second
argument for the intersection of the second argument with the first argument (B ∩ A).
It can be demonstrated in natural language with the equivalences in (11).
(10) Conservativity
DEAB ↔ DEA(B ∩ A)
(11) a. Some students smoke.
≈ Some students are smoking students.
b. All students are lazy.
≈ All students are lazy students.
c. Two students are smart.
≈ Two students are smart students.
Conservativity claims that we can ignore all entities outside of the intersection of A
and B. Compare this with a focus sensitive particle like only in (12). For inspection of
the truth conditions of (12) we must take into account individuals outside of A and B,
because if (12) is true, then no other entity than sailors can smoke. From this it follows
that only doesn’t obey conservativity and isn’t natural language determiner which is
hardly surprising for a linguist, as only can modify any syntactic constituent, unlike
regular determiners which can attach only to NPs.
(12) Only sailors smoke.
Besides the universal constraints on the denotation of natural language determiners as
extension and conservativity, Barwise and Cooper examined some other formal properties
of the binary relations between sets, which are satisfied only by some subsets of
natural language determiners. These conditions thus yield classification of determiners
into subclasses distinguished by these different semantic properties. I will discuss one
such property: Monotonicity.
1.1.3 Monotonicity
The only property of generalized quantifiers which I will discuss in this book allows us to
classify the natural language determiners according to their monotonicity. Monotonicity
is imported to the natural language semantics from mathematics where monotone
increasing are such functions which preserve the given ordering. For natural numbers,
example can be a function like f(x) = x ∗ 2, because for any x and y such as x ≤ y,
f(x) ≤ f(y). Monotone decreasing are such functions, which reverse the ordering, so
if again x ≤ y, f(x) is monotone decreasing, if f(x) ≥ f(y), again an example from
arithmetic would be a function like f(x) = 10/x.
In natural language and particularly in the generalized quantifiers framework, the
monotonicity is determined with respect to both arguments of the determiner: nominal
– A and verbal – B. The monotone increasing and monotone decreasing determiners
6
1 The Frameworks
with respect to the first argument are in (13) and monotone increasing and monotone
decreasing determiners with respect to the second argument are defined in (14).
(13) a. MON↑: If DEAB and A ⊆ A’, then DEA’B
b. MON↓: If DEAB and A’ ⊆ A, then DEA’B
(14) a. MON↑: If DEAB and B ⊆ B’, then DEAB’
b. MON↓: If DEAB and B’ ⊆ B, then DEAB’
Let’s demonstrate the monotonicity properties of some determiners on examples. In
natural language the ordering is usually reducible to entailment and because if x is a dog,
the we can entail that x is an animal, we can classify the determiner some as monotone
increasing on its first argument, as witnessed by the validity of an implication in (15-a).
The determiner all is monotone decreasing on its first argument, as the implication
in (15-b) shows, because the implication goes in the opposite direction: from sets to
subsets.
(15) a. Some dogs bark.
→ Some animals bark.
b. All animals sleep.
→ All dogs sleep.
Some preserves the ordering also on its second argument, see (16-a), as long books ⊆
books , but no reverses the ordering on its second argument, as live in this town ⊇
live in the suburbs of this town , see (16-b)
(16) a. Some linguists write long books.
→ Some linguists write books.
b. No linguists live in this town.
→ No linguists live in the suburbs of this town.
Besides the monotone increasing and monotone decreasing determiners, there is a lot
of determiners which are non-monotone in any of their arguments, good example is the
determiner exactly two in (17).
(17) a. Exactly two students came.
Exactly two people came.
b. Exactly two people came.
Exactly two students came.
c. Exactly two students came late.
Exactly two students came.
d. Exactly two students came.
Exactly two students came late.
The property of monotonicity has been famously first used by Ladusaw (1980) to describe
the distribution of negative polarity items, expressions like English ever or any
which occur primarily in the scope of negation and generally in the scope of monotone
7
1 The Frameworks
decreasing quantifiers (also called downward entailing quantifiers). This is the reason,
why (18-a) is ungrammatical – someone is monotone increasing on both its arguments.
(18-b) is grammatical, because all is monotone decreasing on its first argument, but
monotone increasing on its second argument – see ungrammatical (18-c), unlike no
which is monotone decreasing on both arguments, see (18-d).
(18) a. *Someone has ever been to Mars.
b. All students, who have ever been to Prague, love it.
c. *All students love anything.
d. No student loves anything difficult.
1.2 Formal framework
1.2.1 Language of plurality
In this section I will introduce the tool which I will use as the main formal instrument
in the rest of the book. I presented the generalized quantifiers framework in the last
section as an foreword to the main theoretical tool presented now for two reasons:
1. Generalized quantifiers framework represents a very robust and generally acclaimed
framework which works pretty well in many cases. Although especially for indefinites
it predicts behaviour not attested in natural language. And because I will
describe Czech negative noun phrases which seem (at least in Slavic languages) to
act as indefinites, I will comment on the generalized quantifier framework mostly
critically. But if the generalized quantifiers didn’t exist, then neither of the competing
frameworks which are now so popular in formal semantics, wouldn’t be
on the market either. So I take generalized quantifiers to be a necessary step in
our understanding of the noun phrases meaning. The step against which I will
differentiate Landman’s framework introduced below.
2. In this section I will introduce the framework of Fred Landman which he calls
the Language of Plurality (hence LoP) – the details of the approach can be found
in Landman (1989, 2000, 2004). And I think the main ingredients of LoP can be
very well grasped just on the background of the generalized quantifiers (hence GQ)
approach.
Landman’s LoP is one of the frameworks which erode the uniform treatment of semantics
of Noun phrases. So unlike GQ, where all noun phrases are represented as sets
of sets (of course, there is a classification of NPs according to criteria like monotonicity,
weak/strong force, . . . but this classification isn’t reflected in the lexical entries and types
of various determiners and NPs), LoP treats various types of NPs not uniformly. My
motivation for using LoP is the following:
1. LoP offers a very restrictive interpretation of verbal and nominal negation in the
full blown framework, where each step in the derivation is controlled by the formal
8
1 The Frameworks
definition of the framework – see Appendix. So every formalization of a natural
language sentence can be rigorously built step by step according to the rules of
LoP. I consider this property of LoP very important as it offers a way how to
control sometimes very subtle meaning differences expressed by different formulas.
And I will provide the schematic derivations of the logical forms in LoP for the
most important sentences under scrutiny.
2. LoP integrates formal semantics of number, unlike the GQ, where e.g. both denotation
of singular universal and plural NPs like every boy and all boys get the
same type and denotation – the set of all supersets of the set of boys. This is empirically
wrong for many reasons – one of them is the incompatibility of singular
universal quantified NPs with collective predicates like gather. Compare the unacceptability
of sentence like *Every boy gathered with grammaticality of a sentence
like All boys gathered. It seems that the reason of ungrammaticality of the first
sentence lies in semantics – intuitively collective predicate cannot be applied to
atoms and singular universals quantifier like every boy cannot produce anything
higher than atoms – GQ faces a problem if it represents the meaning of both quantifiers
identically. Of course there are attempts to bring the semantics of number
in Montague’s framework (like Bennett (1976)) but I think that full integration of
the plurality phenomena would lead to such dramatical changes in the GQ theory
that the result would be (overall) quite close to LoP.
As I discussed above, LoP treats various types of NPs differently. We can distinguish
three criteria which cut the landscape of NP semantics:
1. The distinction between scopal noun phrases and non-scopal noun phrases: nonscopal
noun phrases can be entered into event types, scopal noun phrases not. It’s
the distinction between e.g. quantified NPs like every boy and indefinites like a
boy/three boys. The former is obligatory quantified-in, resulting in a wide scope
interpretation with respect to the event variable , the later can be quantified-in
but can also be interpreted under the event variable resulting in a semantics close
to the weak indefinites discussed above. I will address this distinction in detail in
section 1.2.3.
2. The distinction between quantificational noun phrases, definites and indefinites:
Landman (2004) distinguishes these three types according to their starting type
of interpretation:
a) quantificational noun phrases start out as type d, t , t . A short note on
types: Landman differs from the traditional Montague typing because he
uses his d type instead of Montague’s e type for entities and e type for
events. I usually use Landman’s typing but if I do not, it should be clear
from the context and hopefully will not confuse the diligent reader.
b) definites start out at type d
c) indefinites start out at the predicative type d, t .
9
1 The Frameworks
So NPs (representing the three classes respectively) like every boy, the boy and
a boy would have the same type in GQ framework: d, t , t and the following
interpretations:
a) every boy in GQ: {X ⊆ E: BOY ⊆ X }
b) the boy in GQ: {X ⊆ E: BOY ⊆ X } iff | BOY |=11
c) a boy in GQ: {X ⊆ E: BOY ∩ X = ∅}
In LoP the three NPs would obtain the following interpretations (and the types
discussed above):
a) every boy in LoP: λP.∀x ∈ BOY:P(x); the type d, t , t
b) the boy in LoP: δ(λx.BOY(x)) – δ is defined as the maximality operator picking
up the supremum in the denotation: for singular NPs it is consequently
defined only if there is one atom in the denotation of the predicate; the type
d
c) a boy in LoP: λx.BOY(x); the type d, t
3. The distinction in scalar maximalization properties of non-scopal noun phrases: the
distinction between downward entailing maximalization triggers and other NPs. I
will discuss this distinction in the following section.
Before I present the different interpretation of NPs in LoP, I will end this section
by presenting the basic machinery of LoP. Let us assume a Boolean domain with three
individuals in it, as shown in (19). The individuals at the bottom line are singularities,
the atoms of the model; the entities above the singularities are plural entities. In the
Boolean semi-lattice, the domain is partially ordered by , the part-of relation, and
closed under , the sum or join operation. The formal axioms of the model can be
found in the standard accounts of singular/plural distinction (Link (1983), Landman
(1989)), where semi-lattices like (19) are used to model denotations of count expressions.
Concerning the denotation of singular and plural nouns, the singular count nouns (like
DOG) denote a set of atoms or, as in (19), the elements at the very bottom of the
semi-lattice, hence, here a,b,c. The plurals (like DOGS) denote the set of atoms closed
under the sum, that is the set of elements a,b,c, a b, a c, b c, a b c in (19).
(19)
a b c
a b a c b c
a b c
1
In this book I don’t aspire at solving the problem of the right formalization of definiteness. Nevertheless
the logical form in b) raises a question (as correctly pointed out by J. Peregrin) of what happens
when the cardinality of the extension of the predicate | BOY | = 1. In that case according to the
definition in b) the semantic calculation stops, a solution which is closer to Frege’s presuppositional
analysis of definite description than to Russell’s.
10
1 The Frameworks
In Link’s semantics, a singular predicate like BOY denotes a set of singular individuals
only, hence a set of atoms. Pluralization is a closure under sum: *BOY adds to the
extension of BOY all the plural sums that can be formed from the elements of BOY,
as formalized in (20). Besides the pluralization operator * (which is a theoretical tool
for description of plural on nouns), let us assume the group-forming operation ↑, which
is an operation that maps a sum onto an atomic (group) individual in its own right.
Landman (2000)’s definition is shown in (21) and in the tables under I give mechanics
for it to work. The group-forming operation packages pluralities into atoms. According
to (21), ↑ operates in the domain of sums of individuals (assembled from individuals,
henceforth called SUM-IND2
), and its output belongs to the domain of groups (GROUP
in (21)). The same process can be observed in the behavior of bunch denoting nouns like
team, committee or government. Bunch nouns, despite their morphological singularity,
denote plurality.3
(20) *BOY = d ∈ D: for some non-empty X ⊆ BOY: d = X
(21) a. ↑ is one-one function from SUM into ATOM such that:
(i) ∀ d ∈ SUM-IND: ↑(d) ∈ GROUP
(ii) ∀d ∈ IND: ↑(d) = d
b. ↓ is function from ATOM onto SUM such that:
(i) ∀d ∈ SUM: ↓(↑(d)) = d
(ii) ∀d ∈ IND: ↓(d) = d
The framework is illustrated in two tables – (22) and (23), the first table (INDIVIDUAL)
shows how sums are assembled from atoms, the second table (GROUP) demonstrates
how group-atoms are closed under the sum operation too, the pluralization operation
works in the same vein as in the INDIVIDUAL part, but this time it ranges over semantical
opaque "impure" atoms to use Link’s terminology.4
The top row of both sub-domains
represents kinds (more about that special ontological part of the universe later) which
are basically taken as the maximal extension of a property (kind of dogs with three
individuals would be their sum a b c). The second row (in the universe with three
individuals) show sums of atoms and the bottom row is the level of atoms. Kinds of
course belong to sums also but have the maximality distinguishing property unlike other
sums.
2
The domain SUM-IND contains only non-trivial = non-singular sums of individuals.
3
The relationship of domains GROUP and IND is the following: both are domains of individuals
but sortally different, GROUP domain is built from group-atoms and IND is built from singular
atoms. GROUP atoms are not reducible to sums from the IND domain. The empirical motivation
is the distinction between collective and distributive interpretation: the group agens of a collective
interpretation of a sentence like Three gangsters killed a president is e.g. a group atom ↑ (a b c),
not a sum a b c). Thanks again to J. Peregrin for reminding me to explain the difference.
4
In the table GROUP there are missing columns for (i) the group atom ↑ (a b c) and (ii) all the
sums resulting from the combination of this group atom with other group-atoms. The omission is
dictated by the lack of space in the table.
11
1 The Frameworks
(22)
a b c KIND
a b a c b c SUMS
a b c ATOM
INDIVIDUAL
(23)
↑(a b) ↑(a c) . . . KIND
↑(a b) ↑(a c) ↑(a b) ↑(b c) ↑(a c) ↑(b c) . . . SUMS
↑(a b) ↑(a c) ↑(b c) . . . ATOM
GROUP
1.2.2 Maximalization of different NPs
In this section I will briefly discuss the relationship of LoP and pragmatics of implicatures.
It is one of the established hypotheses of current formal semantics, that implicatures
(like scalar implicatures connected to numerals) are cancelable unlike entailments
and (at least some) presuppositions (see Portner (2005, 203) for a textbook overview).
So the meaning of sentence like (24) comprises of at least two parts: asserted (semantical,
entailed) and implicated (pragmatical) meaning. Both of them are paraphrased
in (24-a) and (24-b). The asserted meaning is robust and cannot be changed without
drastic revision of the whole discourse, implicatures on the other hand are defeasible and
open to corrections. Both claims are again demonstrated below (the style of presentation
follows Portner’s textbook):
(24) I drank five beers.
a. entailment: I drank at least five beers.
b. implicature: I didn’t drink six beers.
a’ ??I drank five beers, but I didn’t drink four. (failed cancellation of entailment)
b’ I drank five beers and in fact I drank six. (cancellation of implicature)
The implicatures are derived Grice’s Maxims and because speakers can obey different
maxims, the implicatures are cancelable (see Grice (1989)).
How about LoP and implicatures? First notice that LoP delivers the basic meaning
for sentences with numerical NPs without implicatures, so non-downward, non-upward
entailing numerals are treated without maximalization and consequently their truth
conditions are too weak. Sentence like (25) obtains logical form like (25-a) which claims
that there was an event of leaving with a sum of three boys as its plural agent.
(25) Three boys left.
a. ∃e[LEFT(e) ∧ ∃x ∈ ∗
BOY ∧ Ag(e) = x ∧ |x| = 3]
LoP is a neo-Davidsonian framework working with the explicit event variables (of type
e ) and thematic roles (Agent, Patient, Theme, . . . which are usually used in the shortcut
form in the formulas) which are taken as functions from events to entities, see Appendix
to the current chapter and Landman (2000) for details. Such sentence is compatible
with four, five, six, . . . boys leaving because in such a situation, there of course is an
event of leaving with three boys as an agent. I will address this problem in the rest of
12
1 The Frameworks
the present section but let’s look at another problem first.
It is a problem which faces any Davidsonian theory like Landman’s LoP. It stems
from the fact that existential closure over an implicit event variable (which is part of
any Davidsonian theory) entails existence of something (event or set of some sort if the
theory is translated into second-order logic). But downward entailing quantifiers are
compatible with there being nothing. So e.g. (26) entails the existence of a leaving
event, and there is no such entailment. There are at least two solutions of the problem:
easy and hard solution. Easy solution follows the way of allowing null object into the
semilattice denotation of thematic roles – see Landman (2004) for the implementation.
The hard solution can be found in Landman (2000). As this issue of choosing between
the two options will be not important in my investigations, I leave it aside and will
tacitly assume the null object in the denotation of thematic roles.
(26) At most three boys left.
a.???∃e[LEFT(e) ∧ ∃x ∈ ∗
BOY ∧ |Ag(e)| ≤ 3]
But back to the problem with non-downward, non-upward entailing numerals, which
will be important in the last chapter of the book where we will consider interpretation
of negative manner and especially degree questions. (Landman, 2000, 231) discusses
the issue and follows the established fact that implicatures are cancelable, so the maximality
requirement shouldn’t be part of the semantics proper. Landman’s reasoning
can be demonstrated by the following example. Imagine a scenario with departments
competing for the most rigorous attitude to students – there is a threshold – if during
examination period three professors reject ten students (cumulatively – for the definition
of cumulativity see 1.2.3.1), the department is rigorous enough. In such a context you
can say something like (27).
(27) Our department is rigorous. Three professors rejected ten students, in fact four
professors rejected fifteen students at our department.
But for Landman the maximalization is local, not global as in the classical Grice’s approach
to implicatures. He builds his idea on examples like (28) which show that the
global (Gricean) approach to implicatures results in an inadequate implicated meaning,
especially if we take into account also sentences with numerical NPs in the scope of quantifiers
like every. Gricean implicatures of (28) would mean (as shown in (28-a)), that
there are some professors who didn’t reject three students. (28) doesn’t have such implicature
which signals that the local approach to implicatures would be maybe more appropriate.
In the next section we will see that quantifiers like every obligatory quantify-in
over the event variable and if the implicatures are calculated at the event type, the local
implicatures for (28) are (28-b) which seems to reflect our intuitions correctly.
(28) Every professor rejected three students.
a. Grice (global) implicature: It is not true, that every professor rejected three
students.
= Some professors didn’t reject three students.
13
1 The Frameworks
b. Local implicature: for every professor x: x rejected not more then three
students.
Landman (2000, 236) defines his maximality implicatures in form of the Implicature
Construction Principle (ICP) – see (29). With respect to the local implicatures of
numerical noun phrases, we apply the second point of ICP: in examples like (28) it
delivers us the local negation of stronger alternatives on the scale.
(29) Implicature Construction Principle
1. The core of the exactly-implicature, triggered by a numerical noun phrase,
is constructed at the event type that that noun phrase is in, relative to the
scale constructed there.
2. From the core of the exactly-implicature, the actual implicature of the sentence
asserted is built up, following the semantic composition of the sen-
tence.
3. It becomes an implicature at the sentence level, unless, in the process of
building up, there is a stage where the implicature built up at that stage
is incompatible with or entailed by the semantic meaning built up at that
stage.
But what is the most important point for the purposes of the current book is that
the local approach to implicatures (coded via ICP) predicts that implicatures can be
cancelled during the derivation of the sentence meaning (see point 3 of ICP). Consider
a sentence like (30) where the numerical NP is in the scope of verbal negation. The
schematic derivation of implicatures according to ICP is in (30-a-c). The most important
part is (30-b) where negated entailed meaning contradicts the maximality implicature of
numerical NP and because of that, the implicature vanishes. That again conforms the
intuitions about meaning of sentences like (30), where I think nothing like the maximality
implicature detected in the affirmative sentences arises. This finding will be crucial in
the chapter about negative questions and also in the chapter about the interaction of
scope between negation and other logical operators in the sentence.
(30) There weren’t four boys at the party.
a. Local implicature (at the level of the event type):
meaning: There were four boys at the party.
implicature: There weren’t more than four boys at the party.
b. we add negation scoping over event:
meaning: There weren’t (at least) four boys at the party.
implicature: It is not the case that there weren’t more than four boys at
the party.
= There were more than four boys at the party.
c. the assertion is cancelled because it contradicts the meaning
14
1 The Frameworks
1.2.3 Scopal and non-scopal NPs
Landman’s theory treats non-quantificational noun phrases differently from the quantificational
ones. In that respect it is again one of the theories which erode the uniform
treatment of all types of NPs, as we know it from Generalized Quantifiers framework
of Barwise and Cooper (1981). Beside the technical implementation of the cut between
quantificational and non-quantificational NPs discussed below, the main empirical motivation
for the non-uniformity is the empirical finding that genuine quantifiers like every
or no are obligatory distributive, as witnessed by the ungrammaticality of sentences like
(31) where the distributivity of the quantifier clashes with the collectivity semantics of
the predicate.
(31) *Every student met in Prague.
Non-quantificational NPs like definites, indefinites, numeral headed NPs and proper
names on the other hand are ambiguous between the distributivity and collectivity interpretation,
consider sentence like (32): definites in (32-a), indefinites in (32-b), numerical
noun phrases in (32-c) and proper names in (32-d) all allow both distributive and
collective interpretation.
(32) a. The boy and the girl wrote the letter.
b. A boy and a girl wrote the letter.
c. Two boys and three girls wrote the letter.
d. John and Mary wrote the letter.
Let’s continue with the formal treatment of the non-quantificational/quantificational
split. For Landman, non-quantificational NPs can shift their interpretation from the
plural to the group freely. NPs like John and Mary and three boys have thus two interpretations:
both non-quantificational NPs can be interpreted either as the set of properties
that a sum of three boys (or the sum of John and Mary) have, or, alternatively, the NPs
can be interpreted as the set of properties that a group of three boys (or group of John
and Mary) has. The first interpretation is called sum interpretation and is responsible
for the distributive reading of sentences containing such NPs; the second interpretation
is called group interpretation and is the interpretation of the non-quantificational NPs in
sentences with collective predicates. Unlike the non-quantificational NPs, quantifiers get
their standard interpretation (as in (33)) and their standard interpretation is obligatory
atomic, resulting in the obligatory distributive interpretation of the whole sentence.
(33) John and Mary
a. j m
b. ↑ (j m)
(34) three boys
a. λP.∃x ∈ ∗
BOY : |x| = 3 ∧ P(x) (sum)
The set of properties that a sum of three boys has.
b. λP.∃x ∈ ∗
BOY : |x| = 3 ∧ P(↑ (x)) (group)
15
1 The Frameworks
The set of properties that a set of three boys has.
Quantifiers get their standard interpretation, but in the process of composition with
verb they must scope over the event variable. Negative noun phrases will eventually
be interpreted as indefinites (because negation cannot scope over predicates in the full
fledged LoP) but let us postpone that for a moment.
(35) every girl
a. λP.∀x ∈ GIRL : P(x)
(36) no girl
a. λP.∀x ∈ GIRL : ¬P(x)
In the next section I will show how LoP works on some model cases of sentences with
plurality denoting NPs. For the full demonstration of the system see Landman (2000)
and for the discussion how LoP can be fruitfully applied to various classes of Czech
numerals see Dočekal (2012a).
1.2.3.1 Cumulativity, collectivity and distributivity
In LoP different types of NPs are more or less able to denote different plural meanings.
But the indefinite numerical NPs are ceteris paribus able to denote all three types
of meanings mentioned in the title of the current section. The literature on plurality
unanimously distinguishes between the distributive and collective plurality interpretations.
In some frameworks the distinction is further refined and the third reading
called cumulative is established. Landman (2000) and Scha (1981) are proponents of
the three way ambiguity, unlike Winter (2001) and Roberts (1987) who try to reduce
the cumulative reading to the collective interpretation. I will show in further chapters
that Czech negative noun phrases directly support the three way ambiguity. But before
that let me demonstrate the three types of meanings along with their formalizations in
LoP. Let’s consider now nearly a classical type of sentence like (37) with the three logical
forms in LoP formalizing the three readings. I will comment on each of them in the rest
of the current section.
(37) Three boys kissed four girls.
a. cumulative:
∃e : ∗
KISS : ∃x ∈ ∗
BOY : |x| = 3 ∧ ∗
Ag(e) = x ∧ ∃y ∈ ∗
GIRL : |y| =
4 ∧ ∗
Th(e) = y
b. distributive:
∃x ∈ ∗
BOY : |x| = 3 ∧ ∀a ∈ ATOM(x) : ∃y ∈ ∗
GIRL : |y| = 4 ∧ ∀b ∈
ATOM(y) : ∃e ∈ KISS : Ag(e) = a ∧ Th(e) = b
c. collective:
∃e ∈ KISS : ∃x ∈ ∗
BOY : |x| = 3 ∧ Ag(e) =↑ (x) ∧ ∃y ∈ ∗
GIRL : |y| =
4 ∧ Th(e) =↑ (y)
Let’s first focus on (37-a) – cumulative reading – which in LoP can be paraphrased
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a ----- 1, 2
b ----- 2, 4
c ----- 3
as: there is a sum of kissing events that has a sum of three boys as plural agent and
a sum of four girls as plural theme. The logical form (37-a) predicts that the reading
should be the most natural and salient among the other readings when we consider such
sentence out of the blue. The cumulative (scopeless) reading is basic reading of such
sentences because no operator and no additional rule (quantifying-in and etc) is applied.
One of the situations which would make such reading true is depicted below. By small
letters a, b, c I symbolise different boys (one boy per each letter), by the numerals I
symbolise different girls. As we see, this is scopeless reading in the sense that it’s not
true that for each boy there were four girls and also for no girl there were no three boys
kissing her. The event is pluralized (as formalized by the * operator over event variable)
and both Agent and Theme theta roles are pluralized as well. Although the number of
kissing events isn’t constrained as far as there were three boys and four girls involved in
the pluralized event.
(37-b) is the distributive reading which in LoP arises due to scoping the object,
then scoping the subject over it. And we can paraphrase the reading as: there are three
boys such that for each boy there are four girls such that the boy kisses each of those
four girls. This is the totally distributive reading in the sense that both numerical NPs
are scoped over the event variable and they are scopally dependent with respect to each
other – in this interpretation the subject scopes over the object. The reading is depicted
below
a ----- 1, 2, 3, 4
b ----- 5, 6, 7, 8
c ----- 9, 10, 11, 12
Last type of the reading is the (37-c) – collective reading – which can be paraphrased
as: there is an event of a group of three boys kissing a group of four girls. This is again
scopeless reading but this time the event isn’t pluralized, its atomic arguments are two
groups of three boys and four girls. One of the situations making such formulas true
is depicted below. It’s a bit hard to imagine a situation which would satisfy the truth
conditions of (37-c) with the predicate like kiss. Maybe something like a scenario where
a group kissing event of seven teenagers is taking place in a car would fit best.
(a+b+c) ----- (1+2+3+4)
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So there are three basic types of readings for indefinite noun phrases (and numerical
NPs as one of the major representatives of indefinites). Besides the three readings, we
can also think (for the two NPs containing sentences) of their possible combinations:
Landman (2000) distinguishes eight such readings. I will offer some arguments for distinguishing
collectivity and cumulativity in later chapters, but let’s demonstrate the
distinction in further example. Recall that in LoP cumulativity isn’t a kind of collectivity,
it is a distributive reading without scoping the arguments. (38) sounds weird
because its subject argument cannot be easily interpreted collectively (give birth is very
distributive). But if cumulativity was a subcase of collectivity, then the sentence should
be OK, because it would describe a scenario where a group of fifteen women gave birth
to a group of seven children – this would make sense if we include into the group of
women also nurses, women doctors, . . . where the whole group would be responsible for
giving birth to seven children. But even though I think (38) could be read in such a
context, it’s a bit weird, anyway. And that seems to show that the cumulative reading
(being basic) here leads to the strange flavour of the most salient interpretation.
(38) ?Fifteen women gave birth to only seven children
The last remark in this section concerns the obligatory distributive interpretation of
quantifiers. They are obligatory distributive with respect to the rest of their formula
which doesn’t mean that some other plurality NPs in the formula cannot be interpreted
collectively or cumulatively. Such mixed reading can be one of the interpretations of
(39) (and I assume it’s the most salient interpretation). So because quantifiers like
every boy are able to have only the distributive reading, depending on the interpretation
of object argument, one of the situation verifying (39) is depicted below the formula.
(39) Every boy kissed four girls.
a. ∀x ∈ BOY : ∃e ∈ ∗
KISS : Ag(e) = x ∧ ∃y ∈ ∗
GIRL : |y| = 4 ∧ ∗
Th(e) = y
a ----- 1, 2, 3, 4
b ----- 3, 4, 5, 6
c ----- 5, 6, 7, 8
1.2.4 Negation in LoP
One of the reasons why I adopted LoP is that the scope of negation in LoP (like in
any neo-Davidsonian theory – see e.g. Schein (1993)) is fixed. Negation must outscope
the event variable, otherwise the sentences with negation would have tautological truth
conditions. This can be seen in (40-b), the logical form for sentence like (40-a) which
would arise if we allow negation to scope freely in LoP. The logical form in (40-b)
describes a situation in which there is a walking event which doesn’t have a girl as the
agent, since this is most likely true in any situation, the result is a tautology. But of
course (40-a) doesn’t have tautological interpretation in natural language at all (compare
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it with prima facie tautologies like Girls are girls. Either you sleep or you don’t sleep, ...
This problem does not arise only if negation has wide scope, as in (40-c). This reading
is scopeless (with respect to the interpretation of negative NP) which contradicts the
empiry of English but let’s ignore that aspect for now.
(40) a. No girl walked.
b. ∃e[∗
WALK(e) ∧ ¬∃x[∗
GIRL(x) ∧∗
Ag(e) = x]]
c. ¬∃e[∗
WALK(e) ∧ ∃x[∗
GIRL(x) ∧∗
Ag(e) = x]]
Let me conclude this section with a short comparison of LoP with predicate logic, the
comparison with respect to how each of the theories handles negation. LoP is more
restrictive as to the position of negation and also is different in the way it formalizes
ambiguities of NPs and negation. In predicate logic the ambiguities of negation and
NPs are formalized as various scopes of negation: the negation can scope either over
the whole formula – the usual t, t type, or over a predicate – type-shifted variant of
negation with the d, t , d, t type. In LoP it is the NP which scopes above or below
the negation which remains before the existential closure of the event variable. Compare
the different logical forms for an ambiguous sentence like (41).
(41) All students didn’t come.
a. predicate logic:
(i) ∀x[STUDENT(x) → ¬COME(x)]
(ii) ¬∀x[STUDENT(x) → COME(x)]
b. LoP:
(i) ∀x ∈ STUDENT → ¬∃e[COME(e) ∧ Ag(e) = x]
(ii) ¬∃e[COME(e) ∧ [∀x ∈ STUDENT → Ag(e) = x]]
Note that both (i) readings in predicate logic and in LoP are the ’empty room’ meanings,
while (ii) – again in both frameworks – represent the everything between empty room and
99% of coming students scenario. The relative scopes in both frameworks are the same:
∀ > ¬ means the empty room for sentences like (41) if you quantify over individuals as
arguments of a predicate (as in predicate logic) or over events like in LoP. And similarly
¬ > ∀ would be true/false in the same situations, irrespective of the framework.
1.2.4.1 Verbal negation
Now when we settled the issue of formal properties of negation in LoP, let’s focus on how
the natural language negation fits into the framework. Landman’s answer is: auxiliary
negation must take scope over the event type, while it syntactically is located on verb
(V or T), its semantics is that of a sentence operator of type t, t . That means that he
dissociates the scope of the natural language negation in syntax and semantics. In other
words, even if the verbal negation is outscoped by subject and some adverbials (in the
syntactic structure of English), its semantic scope is different. This style of interpreting
natural language negation is independently postulated in syntactico-semantic theories of
negation and negative concord by Penka (2007) and Zeijlstra (2004). But even though
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I don’t want to compare the mentioned theories with LoP, one thing is pretty clear:
Landman’s motivation for treating natural language negation in this dissociation manner
is different from the Penka/Zeijlstra reasoning. It follows from two independent sources:
first source is the neo-Davidsonian framework which forces the scope of negation to be
over the event variable despite its syntactic realization in the scope of subject NP. The
second one is the maximal simplicity of negation – such solution can have negation with
the only type t, t , instead of multiple types for negation like in predicate logic or in
type shifting theories like Partee (1987).
Technical implementation of the idea is then executed as follows: as the negation is of
the t, t type, when it merges with verb (or auxiliary verb as in English), the local type
mismatches (in case of verb: d, e, t ). That leads to the type-driven scope mechanism
which consists of a type-driven storage mechanism. The stored element is carried along
in the derivation in a store and there is a type-driven retrieval mechanism:
(42) Auxiliary negation niet (not) → ¬ of type t, t
(43) Storage of negation by type mismatch: Negation gets stored if there is a
type mismatch with its complement.
(44) Retrieval of negation by type matching: Negation gets retrieved from store
as soon as the input type matches.
Little illustration of the system: consider a sentence like (45), where we negate a sentence
containing manner adverbial slowly. LoP correctly predicts that the logical form
for such a sentence should be (45-a) where negation outscopes the whole formula and
consequently even the adverb. This has a welcome prediction that something like (45-b),
as a logical form for (45), is impossible. (45-b) corresponds to the reversal of scope between
negation and the adverbial – it would be true in a situation where Peter was an
agent of some slow event which wasn’t the event of walking, e.g. it was an event of
swimming or driving a car. It’s hard to judge only from intuition whether (45) has such
a reading but at least for me this doesn’t seem to be the case.5
(45) Peter didn’t walk slowly.
a. ¬∃e[WALK(e) ∧ Ag(e) = p ∧ SLOW(e)]
b. *∃e[¬WALK(e) ∧ Ag(e) = p ∧ SLOW(e)]
Note that in predicate logic nothing prevents both scopes and if we treat slowly as a
predicate taking adjunct (probably the easiest and close to the empiry option), it’s even
surprising that negation should take wide scope with respect to the adverbial. Predicate
logic formalizations of both scopes (if we would enrich predicate logic with type of events
and use the second-order calculus) would be as in (46-a) and (46-b). This contrasts with
the restrictiveness of LoP: in LoP manner adverbials must modify the event type, the
negation on the other hand scopes over the existential closure of the event type, so (45-b)
5
In predicate logic it would be possible (if the negation would be not only of the t, t type) to negate
just predicate of events SLOW but because LoP doesn’t have such a logical type for negation, (45-a)
and (45-b) are the only two possible readings of (45).
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isn’t an option unlike in predicate logic.
(46) a. ¬SLOWLY (WALK(p))
b. SLOWLY (¬WALK(p))
LoP, as I use it here, predicts that generally all adverbs should scope under negation.
This is a wrong prediction though, as Landman (2000) acknowledges and is invalid at
least for subject/object oriented adverbials and also for speaker oriented adverbials.
Consider (47) and subject oriented adverb in (47-a) and speaker oriented adverb in
(47-b). While (47-a) is ambiguous, (47-b) is I think only interpretable with the wide
scope of the adverbial. This shows that some adverbials can scope even over the negation
and some of them must scope over the negation, unlike manner adverbials.
(47) a. Peter deliberately didn’t kiss Jane.
b. Peter surprisingly didn’t kiss Jane.
Landman (2000, 306) proposes a solution which relies on quantifying-in into scopal
properties. In a nutshell he claims that subject oriented adverbials modify states which
correspond to the events type shifted into states. So sentence like (47-a) would have
logical form like (48) which we can paraphrase as: what Peter was deliberately about is
his having the property/state of not kissing Jane. Because of this event to state type
shifting possibility in LoP also the obligatory wide scope of negation with respect to
manner adverbials weakens – I think we can interpret it as the default strategy: ceteris
paribus (if linearity, focus, . . . doesn’t say otherwise) negation scopes over the adverbial.
But there is always the option of switching the events into states and then negation can
be in the scope of adverbials e.g.
(48) ∃s ∈ [α] : A1(s) = p ∧ DELIBERATE(p, s, C)
where α = λx.x ∈ AT ∧ ¬∃e ∈ KISS : Ag(e) = x ∧ Th(e) = j
1.2.5 Quantifiers and negation
Let’s repeat: the scope of negation in LoP is fixed, ambiguities arise because of various
scopes of NPs/adverbials. But because various types of NPs do have different treatment
in LoP, scoping possibilities of various quantifiers depend on their type. So let’s focus on
different types of NPs, their predicted behaviour and let’s see whether the theory and
the empiry meet.
First, let’s consider indefinites: indefinites in LoP can be interpreted with wide or
narrow scope (corresponding to their sum/group status). That seems to work well –
wide scope of the indefinite corresponds to a specific interpretation (there is a pipe
which John didn’t smoke), the narrow scope corresponds to a non-specific reading (John
can be non-smoker in this scenario e.g.).
(49) John didn’t smoke a pipe.
a. ∃x[PIPE(x) ∧ ¬∃e[SMOKE(e) ∧ Ag(e) = John ∧ Th(e) = x]]
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b. ¬∃e[SMOKE(e) ∧ Ag(e) = John ∧ PIPE(Th(e))]]
Second class of NPs I consider in this section are unambiguous quantifiers. Recall that
they must scope over the event variable, which results in their obligatory distributive
interpretation. I think this prediction isn’t totally right, at least for English every it
seems that both scopes are available. But for each the prediction seems to be correct.6
So while (50) can both have logical form (50-a) and (50-b), where the former represents
the quantifying-in of the universal quantifier over negation (as expected) and the
later represents the universal quantifier in situ (unexpected), (51) seems to have only
the reading where each scopes over the negation leading to the obligatory wide scope
interpretation of the quantifier.
(50) Every boy didn’t come.
a. ∃x[ (BOY (x)) ∧ ∀a ∈ ATOM(x) : ¬∃e[COME(e) ∧ Ag(e) = a]]
b. ?¬∃e[COME(e) ∧ Ag(e) =↑ ( (BOY (x)))]]
(51) Each boy didn’t come.
a. *¬ > ∀
b. ∀ > ¬
It seems that obligatorily distributive quantifiers like each really scope only over negation
but for every this isn’t so clear. One of the options how to handle this problem in LoP
is to weaken the obligatory distributive treatment of the quantifier every. This seems to
be correct, because at least in object positions it’s not hard to find examples of every NP
being interpreted collectively, see (52), where the adverb slowly modifies the maximal
event of the destruction of all shops in the neighborhood, so the object NP must be
interpreted collectively, as in the LoP formalization in (52-a)
(52) TESCO slowly destroyed every shop in our neighborhood.
a. ∃e[DESTROY (e) ∧ SLOW(e) ∧ Ag(e) = TESCO ∧ ∃x ∈ ∗
SHOP ∧
Th(e) =↑ ( (x))]
1.3 Summary
This chapter provided the introduction into Language of plurality – the tool which I
will use most often in the following chapters where I will look at particular problems
concerning negation in different environments of Czech. The formal face of LoP is shown
in the section 1.4, Appendix to the current chapter, and it literally follows the definitions
from Landman (2000, 179-183).
6
Thanks to Louise McNally (p.c.) for helping me to sort the data.
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1.4 Appendix
1.4.1 The Language of Events and Plurality
1.4.2 Syntax of the Language of Events and Plurality
TYPES:
TYPE is the smallest set such that:
1. d,pow(d),e,pow(e),n,t ∈ TYPE
2. if a, b ∈ TYPE then <a,b> ∈ TYPE
• d is the type of individuals, pow(d) of sets of individuals
• e is the type of events, pow(e) of sets of events
• n is the type of numbers
• t is the type of truth values
• <a,b> is the type of functions from a-entities into b-entities
EXPRESSIONS:
We start by specifying the special constants:
Constants
We have the following kinds of constants:
CONd: j, m, . . . individual constants
CONpow(d): BOY, GIRL, . . . nominal constants
INDd, GROUPd, SUMd, D sortal constants
CONpow(e): WALK, KISS, . . . verbal constants
ATOMe, E sortal constants
CONn: 0, 1, 2, . . . numeral constants
CON<e,d>: Ag, Th, . . . thematic constants
Variables: we have a countable set of variables VARa for every type a.
EXPa, the set of expressions of type a, is the smallest set such that:
EXPa:
1. Constants and variables:
CONa ∪ VARa ⊆ EXPa
2. Functional abstraction:
If x ∈ VARa and β ∈ b then λx.β ∈ a, b
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3. Functional application:
If α ∈ a, b and β ∈ a then (α(β)) ∈ b
4. Connectives:
If φ, ψ ∈ t then ¬φ, (φ ∧ ψ), (φ ∨ ψ) ∈ t
5. Identity, inequaility:
If α, β ∈ d then (α = β) ∈ t
If α, β ∈ e then (α = β) ∈ t
If α, β ∈ n then (α = β), (α < β) ∈ t
6. Set formation:
If x ∈ VARd and P ∈ pow(d) and φ ∈ t then {x ∈ P : φ} ∈ pow(d)
If x ∈ VARe and P ∈ pow(e) and φ ∈ t then {x ∈ P : φ} ∈ pow(e)
With this we can introduce other sortal expressions like:
SUMd - INDd, ATOMd = INDd ∪ GROUPd
I will usually drop the type indices.
7. Set application:
If α ∈ d and P ∈ pow(d) then (α ∈ P) ∈ t
If α ∈ e and P ∈ pow(e) then (α ∈ P) ∈ t
8. Quantification:
If x ∈ VARd and P ∈ pow(d) and φ ∈ t then ∀x ∈ P : φ, ∃x ∈ P : φ ∈ t
If x ∈ VARe and P ∈ pow(e) and φ ∈ t then ∀x ∈ P : φ, ∃x ∈ P : φ ∈ t
9. Plurality:
Part-of and sums:
If α, β ∈ d then (α β) ∈ t
If α, β ∈ e then (α β) ∈ t
10. If α, β ∈ d then (α β) ∈ d
If α, β ∈ e then (α β) ∈ e
11. If P ∈ pow(d) then (P) ∈ d
If P ∈ pow(e) then (P) ∈ e
12. If P ∈ pow(d) the σ(P) ∈ d
13. Groups:
If α ∈ d then ↑ α, ↓ α ∈ d
14. Atoms and cardinality:
If α ∈ d then AT(α)∈ pow(d)
If α ∈ e then AT(α)∈ pow(e)
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15. If α ∈ d then |α| ∈ n
16. Singularization and pluralization:
If P ∈ pow(d) then AT(P), *P ∈ pow(d)
If P ∈ pow(e) then AT(P), *P ∈ pow(e)
17. Plural roles:
If R ∈ e, d then *R ∈ e, d
(12), (13) and (15) do not have a corresponding event clause. These could of course
be introduced, but at the moment we will have no need of them.
1.4.3 Semantics of the Language of Events and Plurality
MODELS:
A model for the language of events and plurality is a tuple
M=< D, E, N, R, ⊥, i >
where:
1. D is a domain < D, u, ATOMd, INDd, GROUPd, ↑, ↓> of singular and plural
individuals with groups. D is the domain of individuals.
2. E is a domain of < E, u, ATOMe > of singular and plural individuals. E is the
domain of events.
3. N is < N, <>, the set of natural numbers with the standard order <.
4. These domains don’t overlap and ⊥, the undefined object, is an object not in D,
E or N.
5. i, the interpretation function, is a function from CONa into Da.
Domains based on model M:
• Dd = D ∪ {⊥}
• De = E ∪ {⊥}
• Dn = N
• Dt = {0, 1}
• Dpow(d) = pow(D)
• Dpow(e) = pow(E)
• D < a, b >= (Da → Db, the set of all functions from Da into Db.
6. R, the set of thematic roles, is a subset of D < e, d > (see below).
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Constraints on interpretation function i:
Sortal constants:
• i(INDd) = INDd
• i(GROUPd) = GROUPd
• i(D) = D
• i(SUMd) = [INDd], the i-join semilattice generated by IND.
• i(ATOMe) = ATOMe
• i(E) = E
Numerals:
• i(n) = n
Next we will be concerned with constraints on nominal constants, verbal constants
and role constants. These constraints capture the assumptions about plurality and
thematic role that I have discussed in the previous lectures:
Nominal and verbal constants are sets of atoms:
• Nominal constants: if c ∈ CONpow(d) then i(c) ⊆ ATOMd
• Verbal constants: if c ∈ CONpow(e) then i(c) ⊆ ATOMe
Finally, we constrain thematic role constants. Roles, thematic or non-thematic, are
functions from E ∪ {⊥} into D ∪ {⊥}, partial functions from events into individuals.
Hence, I assume that all roles satisfy the Unique Role requirement:
Unique Role Requirement:
Thematic and non-thematic roles are partial functions from events into individuals.
We have sums both in the verbal domain (sums of events) and in the nominal
domain (sums of individuals). In both domains, sums indicate plurality. I will
assume that roles taking plural events as argument or plural individuals as value are
non-thematic.
R is the set of thematic roles. I assume that thematic roles are only defined for
atomic events, not for sum events. And I assume that thematic roles take only
atoms, individuals or groups, as value, not sums. This is summarized as the Thematic
Role Requirement:
Thematic Role Requirement:
if ROLE ∈ R then:
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1 The Frameworks
1. If e ∈ ATOMe then ROLE(e)=⊥
2. if e ∈ ATOMe and ROLE(e)=⊥ then ROLE(e) ∈ ATOMd
Finally, thematic role constants are interpreted as thematic roles:
Thematic role constants:
if ROLE ∈ CON< e, d > then i(ROLE) ∈ R
This completes the constraints on the interpretation function.
Assignment functions are functions from VARa into Da, and g[x:d] is, as usual, the
assignment at most differing from g in assigning d to variable x.
SEMANTICS:
We define α M,g, the interpretation of α in M relative to g.
1. Constants and variables:
If c ∈ CONa then c M,g = i(c)
If x ∈ VARa then x M,g = g(x)
2. Functional abstraction:
λxa.β M,g=λd ∈ Da. β M, g[xa : d]
3. Functional application:
(α(β)) M, g = α M, g( β M, g)
4. Connectives:
¬φ M, g = 1 iff φ M, g = 0; 0 otherwise.
φ ∧ ψ M, g = 1 iff φ M,g =1 and ψ M, g = 1; 0 otherwise
φ ∨ ψ M, g = 1 iff φ M,g =1 or ψ M, g = 1; 0 otherwise
5. Identity and inequality:
α = β M, g iff α M, g = β M, g and α M, g, β M, g =⊥; 0 otherwise
α < βM, g = 1 iff α < β , 0 otherwise
6. Set formation:
{x ∈ P : φ} M, g = {d ∈ P M, g : φ M, g[x : d] = 1}
7. Set application:
α ∈ P M, g = 1 iff α M, g ∈ P M, g; 0 otherwise
8. Quantification:
∀x ∈ P : φ M, g = 1 iff for every d ∈ P M, g : φ M, g[x : d] = 1; 0 otherwise
∃x ∈ P : φ M, g = 1 iff for some d ∈ P M, g : φ M, g[x : d] = 1; 0 otherwise
Plurality:
Part of and sums:
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9. α β M, g = 1 iff α M, g β M, g; 0 otherwise
10. α β M, g = α M, g β M, g if α M, g =⊥, β M, g =⊥; ⊥ otherwise
11. u(P) M, g = u( P M, g) if P M, g = ∅; ⊥ otherwise
12. σ(P) M, g = u( P M, g) if u( P M, g) ∈ P M, g; ⊥ otherwise
Groups
13. ↑ α M, g =↑ ( α M, g) if α M, g ∈ SUM; ⊥ otherwise
↓ α M, g =↓ ( α M, g) if α M, g ∈ ATOM; ⊥ otherwise
Atoms and cardinality:
Let α ∈ d or α ∈ e:
14. AT(α) M, g = AT( α M, g) if α M, g =⊥; ∅ otherwise
Where AT(x)={a ∈ ATOM : a x}
15. |α| M, g = | AT(α) M, g|
Singularization and pluralization:
16. AT(P) M, g = AT( P M, g) where AT(X) = ATOM ∩ X
∗
P M, g = [ P M, g] where [X] is the i-join semilattice generated by X (and [X]=∅
if X = ∅).
All this is completely as before. The new part comes with the plural roles:
Plural roles
17. ∗
R M, g = λe.
({ R M, g(a) : a ∈ AT(e)}) if ∀a ∈ AT(e) : R M, g(a) =⊥
⊥ otherwise
If e is an event in E, and for every atomic part a of e, thematic role R is defined for
a, then plural role ∗
R is defined for e, and maps e onto the sum of the R-values of the
atomic parts of e.
If thematic role R is not defined for every atomic part of e, then ∗
R is not defined for
e, and ∗
R maps e onto ⊥.
28
2 The nature of negative noun
phrases
2.1 Introduction
The goal of this chapter is to argue that in contrast to n-words in English, Czech n-words
are not quantifiers but they should be analyzed as indefinites in the scope of sentential
negation. One of the most reliable diagnostics for determination of quantifier status in
natural language expression is the ability to appear in so called predicative position. In
contrast to APs and PPs only some nominals may appear in the predicative position;
quantifiers are generally banned from this position (for one of the early formulation of
this constraint see Doron (1983)) as is exemplified in (1) and (2):
(1) John is [AP tall]/[PP in the room]/[NP a teacher]
(2) a. *John is every member of the club.
b. *John is each man.
c. *John and Mary are most students.
d. *John is exactly one teacher.
This ban on quantifiers in predicative positions can be explained quite easily if we
assume classical Montague typing of quantifiers and proper names: quantifiers are of the
d, t , t type and proper names are also of the same type (proper names denote principal
ultrafilters, sets of properties which a given individual has). We cannot combine these
two types d, t , t X d, t , t by functional application as neither of them can be a
function or an argument of the other type.
What is crucial for my argumentation is that we can use the predicative position as
a test for whether something is a quantifier. Interestingly, there are exceptions to this
generalization. Notably, no-NP (’n-words’) may be predicative as in (3).
(3) John is no friend of mine.
According to Partee (1987) quantifiers can appear in predicative position if reanalyzed
as involving lowering of the standard generalized quantifier (e.g. no friend of mine → set
of entities disjoint from the set of my friends). The type-lowering operation is realized
by the type-shifting operator BE: d, t , t → d, t .
(4) BE[α]=λy.α(λx.x = y) (= λy.α({y}))
Consequently, the shifted quantifier can appear as a predicative NP. The meaning of (3)
29
2 The nature of negative noun phrases
in Partee’s system is that John doesn’t have the property BE_FRIEND_OF_MINE
among the set of his properties, which seems to fit.
(5) John is no friend of mine.
What I want to show is that this type shifting solution gives wrong predictions and
we will get better results if we assume that (at least for Czech and probably generally
Slavic) n-words are not quantifiers but their semantic type is predicative ( d, t type).
This chapter is organized as follows. Sections 2.2 to 2.5 outline the basic assumptions
concerning type shifting mechanisms, choice functions and the syntactic structures corresponding
to the different semantic types. Sections 2.6, 2.7 and 2.8 discuss predictions
made by the introduced assumption for the analysis of different phenomena, including nwords
in the predicative and argument positions, the collective interpretation of n-words
and their semantics in the scope of intensional predicates. In section 2.9 I discuss some
open questions. Finally, the section 2.10 offers a review of the arguments presented in
the paper.
2.2 The puzzle
As it stands, Partee’s proposal makes some incorrect predictions. Mainly, as it is clear
from the data, only some quantifiers can appear in predicative position but the proposal
predicts that BE could apply to any quantifier. Partee herself acknowledges this problem
and proposes a remedy in terms of pragmatic restrictions on type-shifting. For a general
critique of her account see Winter (2001) and the next section. As we will see, however,
Partee’s solution cannot account for data from negative-concord languages. Crucially,
the original type shifting strategy overlooks the fact that quantifiers banned from the
predicate position cannot have a collective interpretation and an opaque reading under
intensional predicates (among other things). Czech n-words (as well as English negative
quantifiers as in (3)) are grammatical as predicate nominals:
(6) Petr
Petr
není
not-AUX
žádný
no
můj
my
student.
student
‘Petr is no student of mine.’
But (at least in Czech and at least not in English, although the distinction probably
holds between Slavic and Germanic languages generally) they can have a collective in-
terpretation:
(7) a. Žádní
no
mí
my
studenti
students
nejsou
not-AUX
dobrá
good
parta.
team
‘#No students of mine are good team.’
b. *No students are a good team.
A de dicto reading in the scope of an intensional verb is grammatical for them which
holds for both Germanic – (8-b) from Landman (2004) – and Slavic – (8-a) and (9) from
30
2 The nature of negative noun phrases
Błasczak (2001, p. 224) – languages.
(8) a. Petr
Petr
nehledá
not-seeks
žádné
no
jednorožce.
unicorns
‘Petr is seeking no unicorn.’
b. Dafna
Dafna
zoekt
seeks
geen
no
griffioens.
griffins.
‘Dafna doesn’t seek any griffins.’
(9) Janek
Janek
nie
NEG
szuka
seek-3.SG.PRES
˙zadnego
no-ACC
jednoro˙zca.
unicorn-ACC
‘Janek does not seek any unicorns.’
Moreover Slavic n-words in the scope of intensional verbs allow only de dicto readings
but Germanic languages allow both de dicto and the de re readings. I will show more
about this prediction in next sections. Beside that, uncontroversial quantifiers like ani
jeden student ‘not a single student’, despite having the same truth-conditional import,
contrast with n-words in the way they behave in the mentioned contexts (no collective
reading, ungrammatical in predicative position and only the de re reading in intensional
contexts).
(10) *Petr není ani jeden můj student.
‘*Petr is not a single student of mine.’
(11) Petr
Petr
nehledá
not-seeks
ani
not
jednoho
one
jednorožce.
unicorn
‘Petr is seeking not a single unicorn.’
This shows that there are systematic differences between n-words and quantifiers in
Slavic languages (more differences than in Germanic languages) and moreover that
the difference between n-words and quantifiers cannot stem from semantics only, as
clear from the minimal contrast between quantifier ani jeden student and negative noun
phrase žádný student. In the section 2.3 and 2.4 I will introduce some generally shared
assumptions about types of different noun phrases first and then present two frameworks
formalizing the type-shifting machinery.
2.3 Type shifting
The canonical view on the syntax and semantics of NPs can be summarized as follows:
NPs denote properties (they are semantically of d, t type) type and as such cannot be
straight arguments of predicates. On the other hand they can pretty well stand in the
predicative position and as set denoting expressions can be used to assign some property
to the argument in subject position:1
1
English example in (12-b) is a bit misleading because better would be an example from a language
where in predicative position it’s possible to use bare NP, e.g. Spanish sentence Es profesor de
griego ’He is professor of Greek’ would be a better illustration. Thanks to J. Peregrin for drawing
31
2 The nature of negative noun phrases
(12) a. *[NP Dog] was sleeping.
b. Fido is [NP a dog].
DPs denote generalized quantifiers (they are semantically of d or d, t , t type. Because
of that they can be of course arguments but they usually aren’t well in predicative
positions:
(13) a. [DP Every dog] was sleeping.
b. *Fido is [DP every dog].
In languages like Czech where the distinction between NP and DP isn’t morphosyntactically
coded by determiners, it’s not so easy to say when some phrase is really NP or
DP if no determiner is a part of it. I will have more to say about that later but for
now let’s assume that indisputable quantifiers are usually ungrammatical in predicative
positions and grammatical in argumental ones:
(14) a. [DPKaždý
Every
pes]
dog
spal.
slept
(=(13-a))
’Every dog was sleeping’
b. *Fido
Fido
je
AUX
[DPkaždý
every
pes].
dog
(=(13-b))
’Fido is every dog.’
Usual picture which connects syntax and semantics (see Longobardi (1994, 1996)) follows
an intuition that somehow nouns need determiners to be made into arguments. For
determinerless language like Czech that means that syntactic structure of bare NPs
depends on their function in sentence. If they are arguments then their phrasal status
must be DP and we must postulate some silent determiner turning denotation of <
d, t > type into the right argumental type (either d or d, t , t type). If they are in
predicative position then their type can remain basic d, t .
(15) a. [DP Pes] spal. pes . . . e, t , t
’The dog was sleeping.’
b. Fido je [NP pes]. pes. . . e, t
’Fido is a dog.’
We can propose that bare NPs in languages like Czech are ambiguous with respect to
definiteness/indefiniteness also. The hypothesis would be then that bare NP like pes is
three ways ambiguous:
(16) pes =
a. DOG(x). . . predicate of d, t type
b. λP∃x[DOG(x) ∧ P(x)]. . . indefinite NP, quantifier of the d, t , t type
c. σDOG(x) . . . definite NP of the d type;
my attention to this point.
32
2 The nature of negative noun phrases
2.4 Two Theories of Type Shifting between
Arguments and Predicates
Let me briefly introduce two frameworks which systematically map different types of
noun phrases depending on their argument/predicate position in the sentence and also
depending on their determiner type shifting capabilities (especially in determiner heavy
languages like English, where the second option is deeply grammaticalized). The two
frameworks are Barbara’s Partee type shifting approach as describe in Partee (1987) and
Landman’s adjectival theory of indefinites as defined in Landman (2004).
2.4.1 Partee’s Type Shifting Triangle
First type shifting theory was proposed by Barbara Partee in her influential Partee (1987)
paper. It departs from the uniform treatment of noun phrases semantics (discussed in
the first chapter) in one very important aspect – Partee claims that the basic type of
noun phrases is the simplest (lowest) type which fits the type demands of the sentence,
where the noun phrase occurs. She basically proposes that the three types for noun
phrases we discussed in the previous section – two for argument positions: d (singular
and plural) individuals and d, t , t of generalized quantifies; the third type available
for the interpretation of noun phrases in predicative positions is type d, t of sets of
individuals. The three types are demonstrated in (17) respectively.
(17) a. Peter was sleeping. . . . type d
b. Three girls were sleeping. . . . type d, t , t
c. The visitors were three girls. . . . type d, t
Landman (2004, 20) summarises Partee’s position by the following postulate (the name
reminds us that Partee in fact builds her theory of predication on top generalized quantifiers
theory reaching back to Montague (1973) and Barwise and Cooper (1981)).
(18) Montague–Partee (MP):
MP-principle A – the Generalized Quantifier Theory of determiners:
All noun phrase interpretations are born at argument types.
That means that in Partee’s framework quantificational and indefinite determiners start
their type at d, t , d, t , t type and quantificational and indefinite noun phrases
are born at the argument type d, t , t without any need for type-shifting. Schematic
derivation of the meaning of noun phrases like every dog and three dogs follows in (19)
and (20).
(19) a. every → λQλP.Q ⊆ ATOM ∧ ∀x[Q(x) → P(x)]. . . type d, t , d, t , t
b. dog → DOG . . . type d, t
c. every dog → λP.DOG ⊆ ATOM ∧ ∀x[DOG(x) → P(x)]
type d, t , t
(20) a. three → λQλP.∃x ∈ Q : |x| = 3 ∧ P(x). . . type d, t , d, t , t
33
2 The nature of negative noun phrases
b. dogs → ∗
DOG. . . type d, t
c. three dogs → λP.∃x ∈ ∗
DOG : |x| = 3 ∧ P(x). . . type d, t , t
The same holds also for Partee’s analysis of definite noun phrases which are semantically
composed by the application of the definite determiner to the predicate meaning of NP,
see (21).
(21) the → λQ.σ(Q)
The function that maps Q onto the sum of its elements if that is in Q, and is
undefined if not.
The overall principle behind Partee’s analysis is that noun phrases are born at argument
types and if we find them in predicative positions, this results from their type-shifting
into the set type. Landman (2004, 20) subsumes this line of reasoning as MP-principle-B,
here in (22).
(22) MP-principle B – the Partee triangle
Predicate interpretations of noun phrases are derived from argument interpretation
with type lowering operation BE.
ARGUMENTS PREDICATES
d, t , t
d, t
d
BE
LIFT
IDENT
There are three type-shifting operations used by Partee:
(23) a. LIFT: LIFT[α]=λP.P(α)
b. IDENT[α]=λx.x = α (= {x})
c. BE[α]=λy.α(λx.x = y) (= λy.α({y}))
Noun phrases can shift from d to d, t , t with type raising operation LIFT – e.g.
when d denoting proper name conjoins with a generalized quantifier. They can shift
from d to d, t with type raising operation IDENT – e.g. if proper names are used
predicatively as in sentences like Peter is Napoleon in his office. And finally if we
find quantificational or indefinite noun phrases in predicative position, for Partee that
necessarily means that it was type lowered with the operation BE.
34
2 The nature of negative noun phrases
2.4.2 The Adjectival Theory of Indefinites
The second approach to type shifting is proposed by Fred Landman in Landman (2004).
This is the framework which I will use heavily in this chapter. There are many other
approaches to type shifting, see Chierchia (1998) for a neo-Carlsonian approach, Winter
(2001) for choice function approach and discussion of its merits, and of course Partee
and Rooth (1983) and Partee (1987), where the ideas of type-shifting were laid. I cannot
compare the differences of these frameworks here, so let me pragmatically choose the
Landman’s, because for the purposes of my book it fits best.
Landman modifies Partee’s type shifting framework in one important aspect. His
main idea with respect to the type shifting of noun phrases is explicated in his Adjectival
theory principle (see Landman (2004, 21)) where he reverses the type shifting strategy
for indefinites as proposed by Partee. He calls his approach to type shifting adjectival
theory because his main idea is to treat indefinite determiners and numerals similar
to adjectives. As he acknowledges, this idea isn’t particularly new in formal semantics
and various pieces of inspiration can be found in Link (1983), van Geenhoven (1998),
Krifka (1999) among others. But as far as I can see, Landman is the first to seriously
incorporate the idea into full fledged framework. His adjectival theory principle is stated
in (24).
(24) The Adjectival Theory (AT):
AT=principle A – the adjectival semantics of indefinites:
Indefinite noun phrases are born at the predicate type.
So quantificational and definite determiners are interpreted identically in MP and AT,
as relations between sets and functions from sets to individuals respectively. But as
for indefinites, they start at type d, t in AT, the type of sets of individuals, instead of
d, t , t type of MP. And also indefinite determiners, as well as numerals are interpreted
at type d, t , the same type as the type of adjectives and bare nouns. The composition of
indefinite determiners/numerals with nouns proceeds via intersection operation defined
below in (25). The illustrative derivation of (predicative) meaning for noun phrase like
three girls is in (26).
(25) [NP ADJ NP] → ADJ ∩ NP (λx.ADJ(x) ∧ NP(x))
(26) a. three → λx.|x| = 3 of type d, t
The set of plural individuals consisting of three atoms.
b. girls → *GIRL of type d, t
The set of all plural individuals that consist solely of girls.
c. three girls → λx.∗
GIRL(x) ∧ |x| = 3
The set of all sums of girls each consisting of three individuals.
That means that unlike quantificational and definite noun phrases, indefinites (and numerical
noun phrases as a subkind of indefinites) must undergo type shifting when they
occur in argument positions. This is core of Principle B of AT:
35
2 The nature of negative noun phrases
(27) AT-principle B – the Existential Closure Triangle
Argument interpretations of indefinite noun phrases are derived from predicative
interpretations through type lifting with Existential Closure.
AT comprises of three operations, where two are identical to MP (LIFT and IDENT)
but instead of BE, there is the Existential Closure (EC) operation which reverses the
shifting – instead of type-lowering the argument, we type raise the basic d, t indefinite
type.
(28) a. LIFT: LIFT[α]=λP.P(α)
b. IDENT[α]=λx.x = α (= {x})
c. EXISTENTIAL CLOSURE[α]=λP.∃x[α(x) ∧ P(x)]
ARGUMENTS PREDICATES
d, t , t
d, t
d
EC
LIFT
IDENT
In AT then indefinite noun phrases have two basic interpretations: basic which reveals
in the predicative positions and type raised (via existential closure) which appears in
argument positions – see (29-a) and (29-b) respectively.
(29) a. three girls → λx.∗
GIRL(x) ∧ |x| = 3
the predicative interpretation
b. three girls → λP.∃x[∗
GIRL(x) ∧ |x| = 3 ∧ P(x)]
the argument interpretation
2.4.3 Partee’s pragmatic restriction on type shifting
In this section I will only briefly repeat Partee’s pragmatic argumentation which should
restrict the application of the BE operator. Her argument is aimed at the inability of
every quantifier to appear in predicative position. I think that Winter (2001) quite
conclusively shows that this cannot work, but let’s repeat Partee’s proposal first.
Partee (1987) claims that applying the BE operator to generalized quantifier semantics
of a DP like every student would produce a trivial interpretation (an empty set) unless
the interpretation of the noun student is a singleton set. Partee argues that this clashes
with the presupposition of universal quantifiers in natural language. As according to her
DPs of the form every NP presuppose that their NP complements denote non-singleton
sets. This looks like a plausible interpretation of the ungrammaticality of sentences like
36
2 The nature of negative noun phrases
(30) where the BE operator cannot be used to lower the generalized quantifier to set
interpretation for the following reasons. DP every student of mine presupposes nonsingleton
interpretation of the set denoted by the NP student of mine, so applying the
BE to the DP every student of mine would lead to presupposition failure (if we cancel the
presupposition) or to a trivial interpretation (if the presupposition is accepted and the
BE operator is applied anyhow). A generalized quantifier is of incorrect type to combine
with a proper name, so not applying the BE operator leads to a semantic incompatibility
in a third imaginable scenario.
(30) *Peter is every student of mine.
The trouble with this account, as Winter (2001) shows, is that it isn’t able to explain
the argument/predicate asymmetry of the presupposition defeasibility. As the following
example (31) shows, in argument position the non singleton presupposition of the every
NP phrase is defeasible but in predicate position the same presupposition cancellation
doesn’t work. The example shows the singleton interpretation of every NP is available
(even if pragmatically strange) when the DP is in subject position. Moreover both
sentences denote the same situation but the acceptability of (31-a) is based solely on
the argument syntactic position of the quantifier. That means that the non singleton
meaning constraint for the big quantifier is probably only conversational implicature,
not from the presupposition, as presuppositions cannot be generally suspended this way
as in (31-a).
(31) a. If John and Mary failed entry exams, and Peter didn’t, then every student
of mine is Peter.
b. *If John and Mary failed entry exams, and Peter didn’t, then Peter is every
student of mine.
The grammaticality of (31-a) is predicted if we assume that in predicative position the
proper noun can be type lifted to set type ( d, t – the set of all things called ’Petr’)
which is then fed as an argument to a generalized quantifier in the subject position. This
strategy isn’t available when the proper noun is in subject position.
I will show in the next section how the ungrammaticality of every NP in predicative
positions can be explained without the type shifting operator BE. The solution will also
explain the puzzles mentioned at the beginning of section 2.2.
2.5 Linking Syntax and Semantics of Type Shifting
In the rest of the current chapter I will mix Landman’s general approach to type shifting
with Winter’s Flexible Boolean Semantics. The motivation for this move is the sensitivity
to syntactic status of the determiner in noun phrase. Such sensitivity is built into Flexible
Boolean Semantics (hence FBS further). Recall the different behaviour of žádný and ani
jeden in (6) and (10) – the first type of determiner can head noun phrase occurring in
predicative position, the later not. The reason for this lies in the syntactical complexity
37
2 The nature of negative noun phrases
of two types of determiners. But let me introduce FBS now. FBS is developed in
papers Winter (2001) and Winter (2005), a.o.,FBS uses ideas about the semantic layers
within DP that distinguish between a predicate denoting layer and a quantifier denoting
layer. My main assumptions are the following: there are three syntactic layers in DP,
for English from Winter (2005, Figure 1), see (32).
(32) DP
SPEC D
D
some
NP
SPEC
the a
N
Nominals are classified into three types according to the portion of the NP/DP structure
they fill:
1. Nominals that contain a full spec-DP position. These nominals can only be analyzed
as DPs. They appear only in argument positions.
2. Nominals that contain an empty spec-DP and a full D position. These nominals
can be analyzed as either DPs or D s. They can only appear in predicate positions
with overt copula.
3. Nominals where both spec-DP and D are empty. These nominals can be analyzed
as DPs, D s or NPs. They can appear only in predicate positions.
There is syntax-semantics matching for these layers:
1. Under their NP analysis, nominals unambiguously denote predicates (type d, t ).
2. Under their DP analysis, nominals unambiguously denote generalized quantifiers
(type d, t , d, t , t before adding a NP argument to a determiner and d, t , t
after applying the determiner to the NP argument).
3. Under their D analysis, the interpretation of nominals is free to move back and
forth between predicates and quantifiers. The example (34), table Indefinites,
represents an instance of such a D -level predicate (a good example from English
is e.g. an NP headed by an unstressed determiner some).
Some illustrations of the system are the following:
38
2 The nature of negative noun phrases
(33)
Proper names
D
D NP
SPEC N
Mary
Predicates
NP
SPEC
a
N
student
(34)
Quantifiers
DP
SPEC
every
D
Indefinites
D
D
some
NP
For English n-words Winter (2001) assumes that in argument positions they are negative
quantifiers (generalized quantifiers) and that they are syntactically rigid nouns. Their
syntax and semantics is the following:
(35)
English n-words
DP
SPEC
no
D
no’(X)(Y) iff X ∩ Y = ∅
= ¬∃x[X(x) ∧ Y (x)]
Compare this with Landman’s treatment of English negative noun phrases in chapter
39
2 The nature of negative noun phrases
1. For now I will simply assume that it’s right to assume that English negative noun
phrases are quantifiers, but see Penka (2007) for careful discussion pointing to another
solution.
2.5.1 Choice functions
The flexible interpretation of the D level is by virtue of phonologically covert operators
that apply at this level and map predicates to quantifiers and vice versa. These operators
are called category shifting principles.
Winter (2001) proposes two such principles: the choice function (CF) operation that
maps predicates to quantifiers, and the minimum operator that maps quantifiers to
predicates. Let’s assume the following common definition of CFs, where they are used
as category shifting principles from predicates to entities (Winter (2001) proposes a more
general framework where CFs are operators from predicates to generalized quantifiers,
but for simplicity I adopt a more intuitive definition from Winter (2005, def. 1)):
(36) For any set E, a choice function over E is a function that maps every non-empty
subset A of E to a member of A.
The opposite of the choice function is the Minimum operator which maps quantifiers to
predicates (it produces e.g. the minimal set from conjunction of two principal ultrafilters
– min(M J) = {{m’,j’}}):2
(37) Minimum sort
min(τt)(τt) = λQτt.λAτ .Q(A) ∧ ∀B ∈ Q[B A → B = A]
The main motivation for using CFs is more systematic treatment of the wide scope
behavior of indefinites.
(38) If some relative of mine dies, I will inherit a house.
a. [∃f[CH(f) ∧ DIES(f(RELATIV E_OF_MINE))]] →
INHERIT(I, HOUSE)
b. ∃f[CH(f) ∧ [DIES(f(RELATIV E_OF_MINE)) →
INHERIT(I, HOUSE)]]
As is well known, indefinites give the appearance of scoping out of syntactic islands, as
in the example (38), cited in Reinhart (1997) with two readings: in (38-a) the existential
closure takes place withing the antecedent of the conditional and we get the „narrow
scope“ reading, but in (38-b) the existential closure takes scope over the conditional and
this results in a „wide scope“ reading.
Existential closure is a mechanism for interpreting indefinites in argument positions
and the logic behind it is a second order quantification over choice functions. According
2
I use the polymorphic conjunction symbol from Winter (2001): conjoins propositions and generalized
quantifiers (as in this case) too.
40
2 The nature of negative noun phrases
to Reinhart (1997) and Winter (2001) this closure can take place at any level of syntactic
structure. This leads to apparent wide scope effects with indefinites.
If we compare Landman’s AT with Winter’s FBS right now, we see that FBS is more
liberal – there is the minimum sort operator which maps quantifiers to predicates, in
this respect it is parallel to Partee’s BE type lowering operator. Unlike Partee, Winter
restricts the usage of minimum sort syntactically as we will see immediately. I will
use Landman’s Existential Closure type shifting operator instead of the mechanism of
choices functions, because the power and the glory of choice functions lies in its ability
to describe wide scope reading of indefinites. And as the issue of wide scope reading
isn’t main topic of my investigation, I will use more conservative Existential Closure
formalisation further.
2.5.2 Czech n-words
For Czech (and I assume generally for Slavic but that would need of course careful
research) I assume basically an indefinite structure for n-words and corresponding to that
indefinite semantics. In the Flexible Boolean Semantics of Winter there’s a question if
Czech n-words are more like English some indefinites (D ) or like (NP) a/the (in)definites.
Winter (2005) proposes a criterion to distinguish between the D and the NP level:
conjunctions of singular D are plural, whereas conjunctions of singular NPs inherit their
number features. This is parallel to conjunctions of other predicative categories such as
VP/TP, PP and AP. In (39) we see that Czech negative noun phrases can be conjoined
in argument position with singular agreement on the verb and that they both can be
interpreted as attributes of one individual (unlike jeden indefinites in (39-b) which are
parallel to some indefinites in English).3
We can interpret (39-a) as (40), which shows
that Czech n-words are NP indefinites.4
(39) a. Žádný
No
velký
big
básník
poet
a
and
žádný
no
národní
national
hrdina
hero
dnes
today
nepronesl
not-gave
řeč.
speech
‘#no big poet and no big national hero gave a speech today.’
b. Jeden
one
velký
big
básník
poet
a
and
jeden
one
národní
national
hrdina
hero
dnes
today
*pronesl/pronesli
*give-sg/give-pl
řeč.
speech
3
(39-a) can be interpreted as attributing two properties to one individual but this interpretation isn’t
necessary: (39-a) can mean that we are talking about two different individuals too. In that case I
would prefer plural agreement though which would point at the shift of the n-words to the D’ level.
4
The singular agreement with conjoined NPs is a suggestive piece evidence but not a sufficient argument
for NP nature of n-words. One of the tests which would offer insight into the DP/NP status of nwords
is opaqueness for extraction: DPs are usually taken as opaque for left branch extraction but
NP’s are transparent in this respect, see Bošković (2005) for Slavic languages. But as Abels (2003)
convincingly shows, the left branch extraction data can be explained by remnant movement analysis,
which unfortunately means that locality effects cannot be used as test for DP/NP status of n-words.
And as I’m not aware of any other syntactic tests which can prove or refute the NP status of n-words,
I will stick to the assumption that n-words are NPs even if we are still missing conclusive evidence
for this claim.
41
2 The nature of negative noun phrases
‘A big poet and a national hero gave a speech today.’
(40) ¬∃x[BIG_POET(x) ∧ NATIONAL_HERO(x) ∧ GIV E_SPEECH(x)]
Let’s start with a hypothesis that Czech n-words have indefinite NP syntax and the
indefinite semantics of a determiner is simply zero; the only semantics is set denotation
contributed by NP and see how far this can lead us. There is of course the need of Czech
n-words to be licensed by verbal negation and I assume that some version of syntactic
agreement theory of n-words in the style of Penka (2007) is on the right track.
Under Winter’s approach indefinites are flexible nominals (predicates) and as such
can be type-shifted into quantifiers in some syntactic constructions. This shifting is
obligatory every time when n-words are in argument positions, as their set d, t type
would lead to type incompatibility in any argument position. As said at the end of 2.3, I
will use Landman’s Existential Closure type shifting operation for this purpose, instead
of Winter’s choice function approach, because as far as I can see, both approaches give
the same truth conditions at least for the cases I will consider in this chapter. And
because Landman’s Existential Closure is lighter in terms of formal machinery involved,
I prefer it for simply parsimonious reasons.
As predicates we would expect n-words to appear in predicate positions. In contrast,
quantifiers of the ’not a single one’ type are rigid nominals and cannot be shifted
into predicates in Winter’s framework. There is no type lowering operator in Landman’s
framework, so both approaches give the same predictions with respect to the ani
jeden/žádný distinction. The distinction between n-words and ’not a single one’ quantifiers
is at least partially syntactic, as n-words belong to the flexible nominals type and
quantifiers to the rigid nominals type in Winter’s system. I think that this is the right
hypothesis as there’s no semantic distinction between both types in Generalized quantifiers
theory. From the point of view of truth conditions, both n-words and negative
quantifiers of the ’not a single one’ type can be correctly represented as an operation
of an noninteresction of any two sets. But if we look more carefully at the syntactic
and semantic behavior of n-words in different environments, we will see that predicate
semantics and NP syntax, as is depicted in (41), predicts their properties much more
correctly. And this is exactly what I will show in sections 2.6, 2.7 and 2.8.
(41)
Czech n-words
NP
SPEC
žádný
N
2.6 Prediction I: predicative positions
Let’s repeat my main assumption: n-words in the negative concord languages are
restriction predicates ( d, t type) and their type does not change in predicative position.
42
2 The nature of negative noun phrases
From that it follows that their appearance in predicative position is expected as their
type is similar to other predicates like syntactic APs, PPs, etc. If n-words were be
generalized quantifiers (sets of sets), it would be predicted that they shouldn’t appear
in predicative positions.
N-words in argument position are interpreted through type shifting via Existential
Closure into the type of generalized quantifiers. So n-words are indefinites of a special
sort (for a closely related proposal see Penka (2007); Zeijlstra (2004); Błasczak (2001)).
N-words can appear in the predicative nominal constructions (they are not quantifiers
there) but the question is why quantifiers of the every type cannot occur in this position
as well if the flexible Boolean semantics has the minimum operator as in (37). In
Winter’s system this follows from a syntactic ban on type shifting rigid DPs. The min
operator can shift quantifiers to predicates (e.g. principal ultrafilter) if they are flexible.
In Landman’s framework the possibility of lowering quantifiers to predicates is entirely
absent.
On the other hand, quantifiers of the ’not a single one’ type are rigid nominals, so in
predicative position they would need min operator to turn them into set type; but this
type shifting is forbidden as they are rigid nominals, they are DPs and their logical type
cannot be shifted.
Czech n-words are grammatical in predicative positions and moreover they can have
a distributive reading there as in the following example. As they are interpreted as
predicates, they can be conjoined by boolean conjunction and the proper name Petr in
the subject is interpreted as a set of sets (type shifted by the LIFT type raising operator
from the simple d type to the d, t , t ) and is applied to them.5
The result then
is logically equivalent to the conjunction of two predicates applied to a term denoting
the atom individual Petr. If the n-words in (42) would be quantifiers, then the boolean
conjunction of them would assemble the set of properties common to both quantifiers
and this set would be applied to the subject. This would lead to the same type problems
discussed in Section 2.2 for simple quantifiers in predicative position.
(42) Petr
Petr
není
not-AUX
žádný
no
můj
my
kamarád
friend
ani
neither
žádný
no
můj
my
soused.
neighbor
‘Petr is no friend of mine and no neighbor of mine.’
a. ¬λP.P(Petr)(FRIEND_OF_MINE ∧ MY _NEIGHBOUR)
⇐⇒ ¬FRIEND_OF_MINE(petr) ∧ ¬MY _NEIGHBOUR(petr)
2.7 Prediction II: collectivity
My basic hypothesis is that n-words in negative concord languages like Czech are
5
The conjunction ∧ in (42) is not of the standard type t, t , t type but it is a predicate conjoining operator.
In the example it joins two sets and outputs their intersection: λx.[friend(x)∧neighbour(x)].
The whole sentence is then true if the set of sets (set of Peter’s properties – formalizing the proper
name Petr) doesn’t contain as one of the sets, the intersection. For the definition of such polymorphic
conjunction see Winter (2001:36). Thanks to J. Peregrin for reminding me of the difference
between the predicate conjunction and the propositional conjunction.
43
2 The nature of negative noun phrases
simply indefinites which must syntactically agree with verbal negation and this negation
is the locus of the logical negation interpretation.
As indefinites, n-words denote set(s) of objects (depending on their morphological
number) and we should expect them to be grammatical with collective predicates which
demand plural arguments. On the other hand if n-words would be generalized quantifiers
(at least in classical Montague typing) we wouldn’t expect them to be grammatical
with genuine collective predicates. Recall that in LoP unambiguous quantifiers like
every/each must scope over the event variable which leads to the obligatory distributive
interpretation.
In this section I will look at behavior of n-words with collective predicates. There
are two sentence types which are important in this respect. The first one (example
(43)) will be dealt with in the subsection 2.7.1. (43) is an interesting sentence because
predicates like be a good team are a good testing ground for the quantifier/set type of
their arguments. Basically all quantifiers are banned as their arguments, as (44-b) shows,
which is behavior not shared by all collective predicates (e.g. the collective predicate
meet allows as its arguments quantifiers if they are plural – see (44-a)).
(43) Žádní mí studenti nejsou dobrá parta.
no my students not-AUX good team
‘#None students of mine are good team.’
(44) a. All the students are meeting in the hall.
b. *All the /exactly four/between four and ten/at least ten/many/no/most of
the students are a good team.
The second sentence type (example (45)) will be treated in the subsection 2.7.2. Once
the empirical claim that Czech n-words are capable of collective and cumulative interpretation
is established, I will further explore the differences between English and Czech
negative NPs and also formalize the distinction in LoP – see 2.7.3.
(45) Žádný
no
můj
my
student
student
a
and
žádný
no
můj
my
učitel
teacher
se
REFL
v
in
Praze
Prague
nesešli.
not-met
‘No student of mine and no teacher of mine met in Prague.’
2.7.1 Groups
Recall that Landman (1989) proposes that nouns referring to sets can be shifted to
group denoting atoms in a way that the former plurality is interpreted as an atom
element representing the relevant group of objects, and as such they can be arguments
of collective predicates, as in (7-a). Their denotation then is similar to singular noun
phrases like the group of students or the committee. Formally this is represented by ↑
operator in LoP.
As everybody working on plurality agrees, predicates in natural language vary as
to what kinds of plural objects they take in their extension. Let’s first look at what
Landman’s framework predicts in this respect. Then I will focus on the question how
44
2 The nature of negative noun phrases
the basic picture can be refined by Winter’s ideas.
First, let’s look at three basic types of predicates in singular number, reflecting the
singular number of their arguments if they appear in syntactically predicative position:
1. distributive predicates like sleep, have blue eyes or walk take only individual atoms;
2. collective predicates like gather or meet take only group-atoms;
3. mixed predicates like write the book or touch the ceiling take both individual atoms
and group atoms, which results in their ambiguous distributive/collective interpretation
depending on the semantics of argument they take;
As for nominals, their denotation can be divided into individual atoms and group
atoms:
1. nominals like student or boy denote only individual atoms;
2. nominals like team, crowd or library denote only group atoms;
This classification is quite intuitive and is able to explain basic incompatibilities of
predicates and their arguments in sentences like #The crowd had blue eyes (group atom
as an argument of individual atom taking predicate) or #The boy gathered (individual
atom as an argument of group atom taking predicate).
I assume (again with most of the researcher, see Sauerland (2003) for discussion of
this issue) that the grammatical number on nouns is interpreted semantically (I use
Landman’s pluralization star * operator for this purpose) but the grammatical number
of verbs is purely a syntactical reflex of agreement between the subject and the verb.
So if we pluralize the arguments of three mentioned predicates, the closure under sum
assembles pluralities depending on the former type of the arguments. And that must
be reflected also in the denotation of the predicate. Let’s illustrate the working of the
system on some sample denotations of the mentioned classes of predicates and nominals.
First let’s look at singular predicates and nominals:
(46) a. sleep = {a,b,c}
b. gather = {↑(a b),↑(b c)}
c. write the letter = {a,b,↑(a c)}
(47) a. student = {a,b}
b. team = {↑(a b c),↑(a b)}
Now let’s look at the plural version of the predicates and nominals:
(48) a. ∗
sleep={a,b,c,a b,a c,b c,a b c}
b. ∗
gather={↑(a b),↑(b c), ↑(a b) ↑(b c}
c. ∗
write the letter={a,b,↑(a c),a b,a ↑(a c),b ↑(a c),a b ↑(a c)}
(49) a. student = {a,b,a b}
b. team = {↑(a b c),↑(a b), ↑(a b c) ↑(a b)}
45
2 The nature of negative noun phrases
Now, when the basic assumptions behind the plurality interpretation of predicates and
nominals were introduced, let me continue to Winter’s ideas about refining this hypothesis
(note that Winter (2001) doesn’t agree with Landman’s two domains approach –
Winter tries to do without group subdomain of pluralities, that will be reflected by
different formalizations below).
The basic assumptions about collective predicates like be a good team in Winter’s
flexible Boolean semantics is that they are atom predicates where each atom denotes a
plural entity. And according to him, these predicates are genuine collective predicates.
The distinction between collective predicates like be a good team and distributive predicates
like laugh is that distributive predicates are atom predicates as well but in their
uninflected denotations they range only over regular individuals.
Winter’s typology of semantic number classifies predicates according to their behavior
in sentences like the following.
(50) a. all the/no/at least/many students/committees PRED
b. every/no/more than one/many a student/committee PRED
PRED is a predicate (verb, noun or adjective) like be a good team or laugh. If the
sentences in (50-a) and (50-b) are equally acceptable and, if acceptable, are furthermore
semantically equivalent, then PRED is called an atom predicate. If the sentences differ
in either acceptability or truth-conditions, then PRED is called a set predicate.
According to this criterion, a collective predicate like meet is a set predicate but
collective predicate like be a good team is an atom predicate, compare (51-a) and (51-b)
with different acceptability and (52-a) and (52-b) with similar (un)acceptability. All
distributive predicates (like laugh, smile, sleep) are of course atom predicates. What is
the crucial distinction between Landman’s and Winter’s typology of plurality denoting
expressions? From the point of view of collective nouns, it’s Winter’s observation that
not all collective predicates behave similarly – while both be a good team and meet would
be classified as group denoting nominals by Landman, only the first is genuine collective
predicate for Winter, because the second nominal can take also sums in its denotation
(next to group atoms).
(51) a. All the/no/at least two/many students met.
b. *Every/*no/*more then one/*many a student met.
(52) a. *All the/*no/*at least two/*many students are a good team.
b. *Every/*no/*more then one/*many a student is a good team.
Winter’s system builds on the distinction between the semantic number of a predicate
(the atom/set distinction) and the morphological number of the predicate (the sg./pl.
distinction), see (53) and (54). In (55) are some lexical entries for illustration. The
first two principles are analogical to Landman’s pluralization star operator plus the basic
categorization of individual atom and group atom denoting classification. Winter’s
innovations are of two kinds: first Winter doesn’t assume that there is a totally productive
mapping between sums and groups – see the lexical entry for committee; second
he allows also sums into the extension of predicates like meet. This comes from his
46
2 The nature of negative noun phrases
test for atomic/set type of predicate mentioned above. I think this is right move, as
quantifiers are really sensitive to the semi-collective/genuine collective distinction as we
saw in (44-a).
(53) Principle 1 When uninflected for number, atom predicates denote sets of
atomic entities. Uninflected set predicates denote sets of sets of atomic entities.
(54) Principle 2 Number features change the semantic number of predicates so that
all singular predicates denote sets of atoms whereas all plural predicates denote
sets of sets.
(55) a. student’={j’,m’,p’}
b. students = {{j’},{m’},{p’},{j’,m’}. . . ,{j’,m’,p’}}
c. committee’={c’A,c’B}
d. is_a_good_team={c’A,c’B}
e. meet’={{j’,m’},{c’B}}
If we accept classical Montague’s treatment of quantifiers then there’s a type problem
because there is no semantic difference between the singular and plural determiner quantifiers
(all, every, nosg, nopl, . . . ). All of them are of the type d, t , d, t , t but in
Winter’s system (following Bennett) singular predicates are of the d, t type although
plural predicates are of the d, t , t type. Given these assumptions, plural marked arguments
of a quantificational determiner yield a type mismatch and should yield prima
facie uninterpretability.
The situation is rescued via a special interpretation rule called „determiner-fitting“
triggered by the presence of morphological plurality. The working of ‘dfit’ is a bit
complicated but let’s say that it can explain the distinction between (57-a) and (57-b).6
An important prediction of the system is that quantifiers are incompatible with genuine
collective predicates like be a good team (even if the quantifiers are in plural). They
are compatible with set predicates like meet via the dfit strategy but this strategy is
unavailable to rescue grammatically for collective atom predicates.
(56) Determiner fitting
dfit = λD(et)(ett).λAett.λBett.D(∪A)(∪(A ∩ B))
(57) a. All students met in the hallway.
b. *All students are a good team.
Nevertheless some at first sight quantifiers can be subjects of these atom collective
predicates like be a good team, see (58), they are quantifiers of the flexible type (their
6
Dfit is a type shifting operator which essentially allows combination of otherwise distributive quantifiers
(like exactly five boys, which is of two-sets of individuals input type: d, t ) with a collective
predicate like gather (of type d, t , t ). The semantical composition has two steps: first the NP
and VP argument denotations are intersected (for a sentence like Exactly five students gathered there
the output would set of sets of gathered students). In step two, the NP denotation and the output
of the intersection from step one are unionized. Both arguments of the distributive quantifier are
now pure sets ( d, t type), so the quantifier can apply to them without any problems.
47
2 The nature of negative noun phrases
syntactic projection is only D , not a full DP), so they can be type shifted into a set
type and then turned into groups.
(58) a. The students are a good team.
b. Some students I know are a good team.
c. Five students I know are a good team.
As groups they are eligible arguments for genuine collective predicates like be a good
team. The sample derivation of denotation of NP like the students is shown below. In
(59-a) the bare plural students denotes set of atoms and sums, in (59-b) application of
the maximalization σ-operator (the meaning of the definite article) turns the denotation
into the supremum – the maximal entity in the denotation of plural NP students, in
(59-c) we type-shift the supremum into a group using Landman’s ↑-operator, and in
(59-d) we apply the genuine collective predicate to the group. Winter (2001) generalizes
that for rigid nominals the mapping to group-atoms is not available but for flexible ones
it is, this is the reason of ungrammaticality of (57-b) and grammaticality of (58-a-c).
(59) a. students={a,b,c,a b,a c,b c,a b c}
b. the students={a b c}
c. the students (as a group)={↑(a b c)}
d. BE_GOOD_TEAM(↑(a b c)) (=meaning of (58-a))
If we return to the example (43), repeated below as (60), we can say that the system
predicts that it can be grammatical only if the n-word isn’t a generalized quantifier and
rigid nominal. So this is another piece of puzzle which points at the predicate nature of
n-words.
(60) can be formalized as (61), which in LoP says, that there is no plurality in the
denotation of plural nominal students, which could be true group-shifted argument of
the genuine collective predicate BE_GOOD_TEAM.
(60) Žádní
no
mí
my
studenti
students
nejsou
not-AUX
dobrá
good
parta.
team
‘#No students of mine are good team.’
(61) ¬∃x ∈ ∗
STUDENT : BE_GOOD_TEAM(↑ (x))
The corresponding English sentence in (62) is ungrammatical. That shows that English
n-words are at least syntactically rigid nominals, read DPs, and because of that unlike
Czech n-words they cannot be mapped to impure atoms.
(62) No students are a good team.
2.7.2 Coordination of n-words
The next important piece of data is exemplified by sentence (63) which shows that
with set predicates n-words can assemble a plural entity with a property assigned to
48
2 The nature of negative noun phrases
them by the set predicate. This property is then negated because of the propositional
negation (signalized by negative concord both on the n-words and on the verb).
The generalized quantifiers approach cannot explain this sentence interpretation because
the basic denotation of negative quantifiers in GQ theory is a disjoint operation
on sets (no student of mine would denote a set of sets disjoint from my students) and
the only meaning which GQ theory can assign to (63) would be that some intersection
of a set of entities disjoint from my students and teachers met in Prague. That is of
course a very implausible reading for (63).
In Partee’s type shifting system the truth conditions would be similar to the GQ
treatment. (63) would mean that some non-student of mine and some non-teacher of
mine met in Prague, again a wrong meaning for the sentence (63). This also supports the
syntactic theory of negative concord phenomena, as proposed in Penka (2007), because
the scope of negation is interpreted at the propositional level and the scope of n-words
is interpreted under the collective predicate meet (first there is summation of the two
indefinites which is type shifted into a group – about the group consisting of any atom
of student with any atom of teachers, it is said that the group doesn’t belong to the
denotation of the collective predicate meet).
But if we follow the main line of argumentation here and treat n-words as indefinites,
the intuitive meaning of (63) is that for any chosen pair consisting of my student and my
teacher, this pair don’t have a property MET_IN_PRAGUE which is exactly what (64)
formalizes. As the grammatical judgment in English translation shows, this sentence is
either ungrammatical in English or it has the peculiar meaning discussed in the preceding
paragraph, which probably leads to its unacceptability.
(63) Žádný
no
můj
my
student
student
a
and
žádný
no
můj
my
učitel
teacher
se
REFL
v
in
Praze
Prague
nesešli..
not-met
‘#No student of mine and no teacher of mine met in Prague.’
(64) ¬∃x ∈ STUDENT : ∃y ∈ TEACHER : MEET(↑ (x y))
2.7.3 Negative NPs in Czech and English and their formalization
in LoP
As was demonstrated in the previous sections, 2.7.1 and 2.7.2, Czech and English differ
in the way they distribute (English) or don’t allow to distribute (Czech) the pluralities
denoted by their negative NPs. Czech negative NPs are always interpreted cumulatively
(and allow the shift to groups), while English negative NPs are interpreted only
distributively. Let’s consider English sentence (65) and its Czech translation in (66).
(65) No women gave birth to twins.
(66) #Žádné
no
ženy
women
neporodily
not-gave_birth
dvojčata.
twins
’No women gave birth to twins.’
Predicate give birth to twins is extremely distributive, its singular and plural denotation
49
2 The nature of negative noun phrases
would be e.g. sets in (67-a) and (67-b). There is no group element either in the singular
or the plural denotation, because even if today the act of childbirth is carried out by
many nurses and doctors helping the mother, we still at least linguistically (and quite
naturally) credit the main responsibility to the mother only. Let’s assume that plural
women (in both languages has the denotation as in (67)), then the English sentence in
(65) is true in such a model (let’s assume that individuals a,b,c are cows e.g.).
(67) a. give birth to twins = {a,b,c}
b. *give birth to twins = {a,b,c,a b,a c,b c,a b c}
(68) *women = {d,e,d e}
Czech sentence like (66) should be true in such a scenario but it is ungrammatical. Why?
There are two options for its interpretation: cumulative and collective. I will discuss
both in details now. The cumulative interpretation is formalized in (69). The trouble
with the cumulative interpretation is that it forces us to understand the Czech sentence
as we would understand an English sentence like (70) which in the cumulative reading
would ascribe one baby from the twins to each mother. (70) is of course totally natural
in the distributive reading, but it lacks the cumulative reading for biological reasons.
(69) ¬∃ex[∗
WOMAN(x) ∧ ∗
GIV E_BIRTH(e) ∧ ∗
Ag(e) = x ∧ ∗
TWINS(Pat(e))]
(70) Jane and Mary gave birth to twins.
The second interpretative option for Czech negative NPs would be to shift the plurality
into group atom. But again, we cannot interpret such a reading for biological reason.
Compare English sentence like (71) which sounds just weird. To sum up: Czech n-words
are of the predicative d, t type and in LoP they scope under the event variable, their
reading is hence cumulative or collective but never truly distributive. But what about
singular n-words? Czech sentence like (72-a) is perfectly acceptable and has the meaning
corresponding to the English plural negative NPs. I assume that this is simply an effect
of grammatical number: as in singular the cumulative reading and the distributive
reading cannot be distinguished, we have here the illusion of distributivity but in fact,
the singular n-word is still under the closure of the event variable, so we don’t have the
genuine distributivity – see the formalization in (71-b).
(71) Jane and Mary as a group gave birth to twins.
(72) a. Žádná
no
žena
woman
neporodila
not-gave_birth
dvojčata.
twins
’No women gave birth to twins.’
b. ¬∃ex[WOMAN(x) ∧ GIV E_BIRTH(e) ∧ Ag(e) = x ∧ TWINS(Pat(e))]
English negative NPs on the other hand obligatorily scope over the event variable, it
carries the logical negation along the way and their interpretation in LoP is (73). I
formalize the plural negative NP as ¬∃x ∈ WOMAN, because it is originally composed
from ∗
WOMAN and Landman’s scopal quantifying-in rule which ranges over all atoms
in the plurality which can be collapsed into ¬∃x ∈ WOMAN – see the next section for
50
2 The nature of negative noun phrases
the explicit account of the composition.
(73) ¬∃x ∈ WOMAN(x) : ∃e[GIV E_BIRTH(e) ∧ Ag(e) = x ∧ TWINS(Pat(e))]
2.7.3.1 English negative NPs in LoP
In this section I will demonstrate how English negative noun phrases compositionally
contribute to the meaning of the sentences in which they occur. The formal treatment
is done LoP and draws heavily from the chapter 8 of Landman (2004). Landman (2004,
p. 176) proposes the following interpretation for nominal negation – see (74). Nominal
negation (of the type d, t , t , d, t , t ) is stored and retrieved as soon as the
derivation reaches one of the admissible types for negation – in this case the type of
generalized quantifiers ( d, t , t ). As the consequence of its types, nominal negation
is interpreted differently in argument and adjoined/predicative positions and allows the
collective interpretation for English NPs in case they occur in the adjoined/predicative
positions. But in the argument positions the negation is a noun phrase modifier interpreted
as λTλP.¬T(P) – its logical type is d, t , t , d, t , t . In adjunct positions the
nominal negation is incorporated auxiliary negation which scopes in the moment when
the derivation reaches the type t , its starting type is then t, t . In Landman’s system
there is no no type shifting of negation (compare with Partee (1987) where neg NP is
interpreted as ATOM - NP ) in a sense that there is a complement interpretation for
negative NPs – negation is always interpreted as classical logical negation but its different
interpretation is a result of different scopes where it occurs. Sample derivation of
English sentence (75) follows next. The negative NP starts its interpretation as a simple
plural predicate in LoP and the negative part of its meaning is stored – (75-a), because
the type of the NP ( d, t ) doesn’t fit any of the admissible types for nominal negation.
(74) nominal negation
no → ¬n where n is t, t or d, t , t , d, t , t
(75) No girls slept.
a. no girls → ∗
GIRL, STORE ¬n
Because the negative NP is in argument position, it must undergo argument shift to
d, t , t type and because d, t , t is one of the input types for nominal negation, ¬n
must be retrieved from the store – (76-a). This is the scopal version of negative NP and
as such scopes over the predicate – (76-b) – and over the event variable.
(76) a. λP.¬∃x[∗
GIRL(x) ∧ P(x)]. . . type d, t , t
b. λxλe.SLEEP(e) ∧ Ag(e) = x. . . type d, e, t
The types of the negative NP and the predicate are incompatible in this step of derivation,
so we apply maximalization (closure of the event variable) – (77-b) and next we
abstract over variable x, turning its type t into the type d, t – (77-c).
(77) a. λP.¬∃x[∗
GIRL(x) ∧ P(x)]. . . type d, t , t
51
2 The nature of negative noun phrases
b. ∃e[SLEEP(e) ∧ Ag(e) = x]. . . type t
c. λx.∃e[SLEEP(e) ∧ Ag(e) = x] . . . type d, t
Then we quantify-in the negative NP and according to Landman (2000, 194) we must
use the rule of scopal quantifying-in which ranges over atoms of the quantified plurality
(the part ∀xn ∈ ATOM(x) in (78)). SQI quantifies α into φ – λ-abstraction is part
of the SQI in fact, α is the scoped operator. Obligatory distributive interpretation of
scoped operators is consequence of this. After application of SQI to (77-a) (α) and
(77-b) (φ) we obtain (79). For easier reading I will use the formalization in (78-a) which
simply substitutes the negation of existential quantifier with universal quantification
over the negated formula (this follows from the predicate logic equivalence of ¬∃xPx
and ∀x¬Px).
(78) SQIn: scopal quantifying-in.
SQIn=APPLY[λx.∀xn ∈ ATOM(x) : φ, α ]
(79) ¬∃x[∗
GIRL(x) ∧ ∀xn ∈ ATOM(x) : ∃e[SLEEP(e) ∧ Ag(e) = xn]]
a. ∀x[∗
GIRL(x) ∧ ∀xn ∈ ATOM(x) : ¬∃e[SLEEP(e) ∧ Ag(e) = xn]]
The obligatory distributive interpretation of quantified NPs (and English negative NPs
seem to behave in all respects like ordinary quantifiers like every NP) is the theoretical
explanation of ungrammaticality of such operators as arguments of cumulative or
collective predicates. So English negative NPs are treated like obligatorily quantifiedin
indefinites with stored negation. Their behaviour follows from that and it explains
the ungrammaticality of the following examples – (80-a) and (80-b) are ungrammatical,
because both NPs must scope over the event variable in LoP and as such must be interpreted
distributively but this of course clashes with the collective interpretation of the
predicate gather.
(80) a. #Every student gathered in the hall.
b. #No students gathered in the hall.
As for the negative NPs in predicative or adjoined positions – the derivation
doesn’t go through the d, t , t type of NP, so negation is retrieved later, after the
existential closure of event variable. An immediate prediction of this assumption is
that cumulative and collective reading of Germanic negative NPs is possible in nonargumental
positions – see Landman (2004, p.177) – which seems to be the case at least
for Dutch. So Dutch allows in its there is constructions the negative NPs to have the
cumulative and collective reading as demonstrated in (81-a) and (81-b) respectively.
(81) a. Er spelt geen meisje in de tuin.
’There was no girl playing in the garden.’
¬∃e[PLAY (e) ∧ GIRL(Ag(e)) ∧ IN(e) = (GARDEN)]
b. Er kwamen drie jongens en geen meisjes samen.
Three boys and no girls gathered.
52
2 The nature of negative noun phrases
What we seem to see is that there is a correlation between the predicative interpretation
of NP and its collective/cumulative reading. The tentative hypothesis can have a form
of an empirical generalization: distributive interpretation disallows predicative type of
NP and conversely cumulative/collective interpretation is the only plural interpretation
of the predicative NPs. Whether such hypothesis should have deeper explanation and
whether it’s empirically correct is something I hope to examine in a future work.
2.7.3.2 Czech negative NPs in LoP
The same semantics as in (74) would give totally incorrect predictions for Czech negative
NPs. This is so for two main reasons: (i) negative force – Czech n-words don’t carry
any real negative semantics (so there is no double negative reading in Czech) and (ii)
no distributive interpretation of Czech negative NPs – there is no distributive reading
of Czech n-words. Basically then we can assume that Czech n-words don’t have the
d, t , t , d, t , t type and their type is d, t . Moreover they don’t store the negation.
Negative force comes from the verbal negation. To formalize this we can use Landman’s
auxiliary negation rule as repeated here in (82) (after Landman (2004, p.174))
(82) Auxiliary negation
niet(not) → ¬ of type t, t
The obligatory presence of verbal negation can be formalized as in (83). So let’s assume
that negation on Czech n-words is simply signal that the argument shift for Czech
negative NPs in argument positions must be done no later then at the point of negating
the existential closure of the event variable.
(83) Czech n-words: argumental shift of Czech n-words is possible only under negated
event variable.
This is a sort of predicative analysis of negative NPs, close to syntactic proposals like
Zeijlstra (2004) but I think this simple rule explains the behaviour of Czech negative
NPs quite well. It explains that lack of negative verb with n-words leads to ungrammaticality:
(84) is ungrammatical because d, t type cannot occur in argument position and
because the predicative NP isn’t existentially closed, the verb and the argument cannot
be combined because of type mismatch: verb is of the type d, e, t , NP of type d, t
and there is no type shifting rule which can repair this. Let’s look now at the derivation
of (85) and the ingredients in (85-a) – negative NP, (85-b) – the predicate and (85-c) –
the verbal negation.
(84) *Žádný
no
chlapec
boy
přišel.
came
’No boy came’
(85) Žádní
no
chlapci
boys
nepřišli.
not-came
’No boys came.’
53
2 The nature of negative noun phrases
a. žádní chlapci . . . λx.∗
BOY (x). . . d, t
b. přišli . . . λx.λe.COME(e) ∧ Ag(e) = x. . . d, e, t
c. ne-. . . ¬. . . t, t
The derivation continues as: the interpretation of negated verb is predicative with the
event argument (the negation cannot apply and is stored in this moment because of the
type incompatibility) – (86). We apply the argument shift (check whether negation is
in the store) to the argumental negative NP – (86-a). And we lift the predicate, so it
can apply in situ to NP – (87-b).
(86) a. ne-přišli . . . λx.λe.COME(e) ∧ Ag(e) = x. . . STORE ¬
(87) a. λP.∃x[∗
BOY (x) ∧ P(x)]. . . d, t , t
b. λT.{e ∈ COME : T(λx.e ∈ COME(e) ∧ Ag(e) = x)} . . . d, t , t , e, t
Next, we apply the predicate to argument (88-a), then do the maximalization (existential
closure of the event variable – (88-b)) and then retrieve the negation because we reach
the t type –(88-c).
(88) a. {e ∈ COME : ∃x[∗
BOY (x) ∧ Ag(e) = x]}
b. ∃e[COME(e) ∧ ∃x[∗
BOY (x) ∧ Ag(e) = x]]
c. ¬∃e[COME(e) ∧ ∃x[∗
BOY (x) ∧ Ag(e) = x]]
The obligatory cumulative interpretation explains why Czech n-words occur as arguments
of cumulative and collective predicates. As arguments of collective predicates,
they undergo the group-shift but they remain in the scope of the existential closure of
the event variable. On the other hand, they resist to be arguments of distributive predicates
as the following examples show: (89-a) is ok under the cumulative interpretation.
(89-b) is the pure collective interpretation. And (89-c) again demonstrates that Czech
negative NPs resist to be arguments of strictly distributive predicates.
(89) a. Žádní
no
pohřebáci
undertakers
nepohřbili
not-buried
víc
more
jak
than
15
15
lidí
people
za
in
den.
day
’??No undertakers buried more than 15 people per day.’
b. Žádní
no
chlapci
boys
neutvořili
not-formed
pyramidu.
pyramid
’??No boys formed a pyramid.’
c. #Žádní
no
chlapci
boys
neměli
not-have
modré
blue
oči.
eyes
’No boys had blue eyes.’
2.8 Prediction III: intensional predicates
Let’s repeat: n-words are indefinites and without additional structure they denote
sets. From it follows that they should be grammatical in environments selecting for sets
or properties. Intensional predicates were argued to be property selecting and we will
54
2 The nature of negative noun phrases
see that this works well with the indefinite status of Czech n-words.
Indefinites in the scope of intensional verbs are generally able to have two readings,
the de dicto and the de re, as (90) illustrates, which can mean either that there are
two criminals such that the inspector must arrest them or that there is a norm for the
inspector to arrest two criminals per week, irrespective of their identity.7
(90) The inspector must arrest two criminals this week.
a. de dicto: norm for the inspector per week is two criminals
b. de re: there are two criminals such that the inspector must arrest them
N-words in negative concord languages like Czech can be interpreted only de dicto in
these constructions as I want to show in this section. Let’s look at (91) and first it’s the
de dicto reading.
(91) Petr
Petr
nehledá
not-searches
žádného
no
jednorožce.
unicorn
‘Petr doesn’t seek any unicorn.’
In Montague’s classical analysis, the de dicto reading would be analyzed as a relation
SEEK between Petr and the intension of a generalized quantifier as in (92-a), in other
words, intensional verbs denote relations between individuals and quantifier intension,
i.e. they are of type s, d, t , t , d, t . This reading is very weak. It expresses that
Petr stands in the SEEK relation to the function which assigns to every possible world
the set of properties that no unicorn has.
It’s because on Montague’s analysis of the de dicto reading, the negation is sitting in
the wrong place. For Montague, the only alternative is to scope it out. But that gives
the de re reading, which is also wrong.
Zimmermann (1993) argues against Montague’s analysis of quantifiers in the scope of
intensional verbs, in favor of an analysis where the complement of SEEK is an intensional
property, rather than the intension of a generalized quantifier.
This is exactly in accordance with the analysis which postulates an indefinite analysis
for n-words and is also one of the main arguments for separating negative and indefinite
part of n-words (irrespective of the negative concord status of the examined language),
as Landman (2004) and Penka (2007) show, because otherwise we would end up with
the same problems as in (92-a) because at the level of properties, the only plausible
analysis of negation is as complementation as in (92-b).That would mean that Petr is
seeking non-unicorns and not that Peter is not searching for unicorns. The most plausible
meaning of (92) is (92-c) where negation takes scope over whole formula
(92) Petr nehledá žádného jednorožce.
a. SEEK(ˆλP.¬∃x[UNICORN(x) ∧ P(x)])(p)
b. SEEK(ˆ(ATOM − UNICORN)(p))
7
The problem of the de dicto/de re interpretation in the scope of modal verbs is one of the big topics
of formal semantics going back at least to Montague (1973). For the discussion of Germanic n-words
and their semantics in the scope of intensional verbs see Penka (2007, chap. 3).
55
2 The nature of negative noun phrases
c. ¬SEEK(ˆUNICORN)(p))
Let’s return to the de re reading of Czech sentences with n-words. It’s easier to test
them when embedding the n-word under modal verbs than under an intensional verb
like seek. Sentence (93) under the de dicto reading means that there’s no obligation for
the inspector to arrest two criminals this week.
But what would be the de re reading? The de re reading would be true in situations
in which the de dicto reading is false. If the norm of work for inspectors says that there
are no criminals, say a murderer and a burglar, which have to be arrested this week, but
only that two criminals must be arrested per week, then (93) under the de dicto reading
is false but under the de re reading is true.
This is so because in the de re reading an indefinite would scope over modal verb
but under negation. This reading is unavailable for the sentence (93), so I conclude
that n-words in Czech don’t have the de re readings. This follows from the predicate
semantic type of Czech n-words. On the other hand in Germanic languages, negative
noun phrases as quantifiers can quantifier raise over the modal verb, which is the reason
for their ability to have the de re reading as well.
(93) Inspektor
inspector
nemusí
not-must
tento
this
týden
week
zavřít
arrest
žádné
no
dva
two
zločince.
criminals
‘The inspector need not arrest two criminals this week.’
a. ¬ must > ∃
b. *¬ > ∃ > must
2.9 Open questions
I have analysed Czech negative noun phrases as indefinites with the need to be licensed by
negation. Indefinites are generally peculiar in their wide scope behaviour (see e.g. Fodor
and Sag (1982),Kratzer (1998), . . . ). Let’s remind ourselves of the contrast between
universal quantifier in (94) and an indefinite in (95)
(94) Jestliže
If
Petr
Petr
koupí
buys
každou
every
knihu
book
v
in
tomhle
this
knihkupectví,
bookshop
tak
then
přijde
will-be-he
na
on
buben.
drum
‘If Petr buys every book in this book shop, then he will be broke.’
a. [∀x[BOOK(x) → BUY (p, x)]] → BROKE(p)
b. *∀x[[BOOK(x) → BUY (p, x)] → BROKE(p)]
(95) Jestliže
If
Petr
Petr
koupí
buys
jednu
one
knihu
book
v
in
tomhle
this
knihkupectví,
bookshop
tak
then
přijde
will-be-he
na
on
buben.
drum
‘If Petr buys one book in this book shop, then he will be broke.’
56
2 The nature of negative noun phrases
a. [∃x[BOOK(x) ∧ BUY (p, x)]] → BROKE(p)
b. ∃x[BOOK(x) ∧ [BUY (p, x) → BROKE(p)]]
It would be appropriate to check the behavior of Czech n-words whether it shows something
similar in this respect. That means, if the n-words demonstrate any wide scope
phenomena similar to the regular indefinites. At first sight this is not true as we see
from (96) with the only grammatical reading in (96-a) and with the logically possible,
very weak, but in the natural language totally ungrammatical reading in (96-b).
(96-b) can be paraphrased as: there is such an x (book) which if Peter doesn’t buy the
x, then he will remain rich. This would be true in a situation where one very expensive
book in the bookshop would make Peter poor, although buying other books would be
harmless for his wallet, but the sentence (96) is much more strong – it says that any
book in this bookshop would ruin Petr.
(96) Jestli
If
si
REFL
Petr
Petr
nekoupí
not-buy
žádnou
no
knížku
book
v
in
tomhle
this
knihkupectví,
bookshop
tak
then
zůstane
remain-will-he
bohatý.
rich
‘If Petr buys no book in this book shop, then he will remain rich.’
a. ¬[∃x[BOOK(x) ∧ BUY (p, x)]] → REMAIN_RICH(p)
b. ∃x[BOOK(x) ∧ ¬[BUY (p, x) → REMAIN_RICH(p)]]
Let’s follow an old practice and describe the fact by a stipulatively named rule and
because it’s just the opposite of the specificity marking of certain, let’s call it unspecificity
marking rule.
(97) Unspecificity marking rule
The n-words in Czech denote a predicate that must be existentially closed under
the scope of verbal negation and also under the scope of any other logical
operator.
The scope possibilities of Czech n-words are very restricted: they must be interpreted
in the scope of negation and moreover in the scope of any other logical expression in
their sentence. This again formally follows from the status of negation in Landman’s
framework. Negation scopes over the event variable, if some expression (noun phrase,
adverbial, . . . ) wants to be scopally interpreted it must undergo quantifying-in which
raises it over the negation. If Czech n-words are interpreted necessarily under the scope
of negation, then by transitivity, they must be interpreted under all scope taking expressions
in their sentence. The following examples demonstrate this claim.
(98) Petr
Petr
si
REFL
nechtěl
not-wanted
vzít
marry
žádnou
no
řeznici.
she-butcher
‘Petr wanted to marry no woman butcher.’
a. ¬ > want > ∃ woman butcher
b. *∃ woman butcher > ¬ > want
57
2 The nature of negative noun phrases
c. * ¬ > ∃ > want
(99) Dva
Two
řezníci
butchers
nezabili
not-killed
žádného
no
vola.
ox
‘Two butchers killed no ox.’
a. 2 butchers > ¬ > ∃ ox
b. *∃ ox > 2 butchers > ¬
(100) Petr
Petr
často
frequently
nejedl
not-ate
žádný
no
řízek.
schnitzel
‘Petr frequently ate no schnitzel.’
a. frequently > ¬ > ∃ schnitzel
b. *∃ schnitzel > frequently > ¬
Last remark: the reason why n-words are incompatible with modifiers of the certain
type is maybe semantic: certain wants to have widest scope but no goes in the opposite
direction. From this it follows that no closure is available and ungrammatically arises.
(101) *Petr
Petr
si
REFL
nechce
not-wants
vzít
marry
žádnou
no
jistou
certain
studentku.
student
‘Petr wants to marry no certain student.’
2.10 Summary
The present analysis of n-words has shown that Czech n-words are of the set type
( d, t ) and their type does not change in predicate position. N-words in argument
position are interpreted as other indefinites through existential closure. The negative
morphology of n-words is only an agreement feature which signals propositional negation
(negative n-words in Slavic languages must be accompanied by a negated verb, where
negation is high enough to have scope over the event variable). So n-words are indefinites
of a special sort.
As predicates of the set type, n-words can be interpreted in opaque contexts selecting
for properties; they can appear in the predicative nominal constructions (they are not
quantifiers there); they can be mapped to the atom element representing the relevant
group of objects and as such they can be arguments of collective predicates; and they
can form summation of their arguments in coordination which is then interpreted as a
generalized quantifier ranging over collective predicates.
58
Summary
The starting point of the investigations in this book was the model-theoretic approach
to negation in natural language, particularly the application of the Language of Events
and Plurality to Czech negation. In this framework I examined four different areas of
natural language where negation leads to non-trivial (and hence linguistically interesting)
problems – especially when we attempt to explicitly model the compositional building
of the truth-conditions of the whole sentences.
The four areas were: interpretation of morphological negation occurring on verb
and/or on noun phrases simultaneously (Chapter 2), interpretation of apparent aspectual
properties of negation (Chapter 3), prediction of the scope possibilities of negation
and other quantified noun phrases in natural language – especially universal quantifiers
(Chapter 4) and finally the cross-linguistic variation with respect to negative manner
and degree questions ungrammaticality.
All these problems surely require more research by linguists and the certainty of
my conclusions holds only relatively to the data I examined. Nevertheless, I think
it’s safe to conclude that the semantics of natural language negation corresponds to
the truth-reverting function of formal logic. All the apparent counterexamples to such
a claim can be explained away if we take into account syntactic agreement and the
logical type of negation which lead to its interpretation at the appropriate place in the
formula (which can be pretty far from its surface position in natural language). The
alleged aspectual shifting properties of negation are simply reducible to its inference
reversal property which makes the telic environments homogeneous. The mysterious
wide scope interpretation of negation with respect to the universal quantifier follows from
the competence between universal NPs and negative NPs, which (with the negation on
verb caused by the negative concord in languages like Czech) express the opposite scope
of negation and the universal quantifier more economically. And finally the negation as
the source of negative manner and degree questions ungrammaticality in English results
from the independent focus-related properties of English and their different distribution
in Czech.
At a more general level, I tried to solve all empirical puzzles of Czech negation which
I came across during my investigation in the most conservative manner (relative to the
framework I have chosen) as I was able to do. All the complications were blamed on
the independent parts of natural language. This is just one of the ways to go, which is
clear from the alternative hypotheses I mentioned in the previous chapters. But it’s the
one which strikes me as the best because of its elegance and simplicity, as no additional
machinery was postulated beyond the tools which were independently needed in other
areas of the natural language semantics.
59
Bibliography
Abels, Klaus. 2003. Successive cyclicity, anti-locality, and adposition stranding. Doctoral
Dissertation, University of Connecticut.
Abels, Klaus. 2005. ’expletive negation’ in russian: A conspiracy theory. Journal of
Slavic Linguistics 13:5–74.
Abrusán, Márta. 2007. Contradiction and grammar: The case of weak islands. Doctoral
Dissertation, MIT.
Barwise, J., and R. Cooper. 1981. Generalized quantifiers and natural language. Linguistics
and Philosophy 4:159–219.
Beaver, David, and Brady Clark. 2003. Always and only: Not all focus-sensitive operators
are alike. Natural Language Semantics 11:323–362.
Beaver, David, and Cleo Condoravdi. 2003. A uniform analysis of before and after. In
Proceedings of SALT XIII , ed. Rob Young and Yuping Zhou. Cornell: CLC Publica-
tions.
Beck, Sigrid. 1996. Quantified structures as barriers for LF movement. Natural Language
Semantics 4:1–56.
Beck, Sigrid. 2001. Reciprocals are definites. Natural language semantics 9:69–138.
Beck, Sigrid. 2006. Intervention effects follow from focus interpretation. Natural Language
Semantics 14:1–56.
Beck, Sigrid, and Shin-Sook Kim. 2006. Intervention effects in alternative questions.
Journal of Comparative German Linguistics 9:165–208.
Beck, Sigrid, and Hotze Rullmann. 1999. A flexible approach to exhaustivity in questions.
Natural Language Semantics 7:249–298.
Beghelli, Filippo, and Timothy Stowell. 1997. Distributivity and negation: The syntax
of each and every. In Ways of Scope Taking, ed. Anna Szabolcsi, 71–108. Dordrecht:
Kluwer.
Bennett, Michael R. 1976. Some extensions of a montague fragment of english. Doctoral
Dissertation, UCLA.
60
Bibliography
Błasczak, Joanna. 2001. Investigation into the interaction between the indefinites and
negation. vol. 51: Studia grammatica. Berlin: Akademie Verlag.
Bošković, Željko. 1999. On multiple feature checking: multiple wh-fronting and multiple
head-movement. In Working Minimalism, ed. S. Epstein and N. Hornstein, 159–187.
Cambridge, MA: The MIT Press.
Bošković, Željko. 2005. Left branching extraction, structure of NP, and scrambling. In
The free word order phenomenon: Its syntactic sources and diversity, ed. J. Sabel and
M. Saito. Berlin: Mouton de Gruyter.
Büring, Daniel. 1999. Topic. In Focus — Linguistic, Cognitive, and Computational
Perspectives, ed. Peter Bosch and Rob van der Sandt, 142–165. Cambridge University
Press.
Chierchia, Gennaro. 1998. Reference to kinds across language. Natural language semantics
6:339–405.
Csirmaz, Aniko. 2005. Semantics and phonology in syntax. Doctoral Dissertation, MIT,
Cambridge, MA.
Csirmaz, Aniko. 2006. Aspect, negation and quantifiers. In Event structure and the left
periphery of Hungarian, ed. K. É. Kiss. Dordrecht: Springer.
Doron, Edit. 1983. Verbless predicates in Hebrew. Doctoral Dissertation, University of
Texas, Austin.
Dočekal, Mojmír. 2011. N-words: Predicates or quantifiers? In On Words and
Sounds: A Selection of Papers from the 40th PLM, 2009, ed. K. Dziubalska-Kołaczyk
K. Dębowska-Kozłowska, 148–172. Newcastle upon Tyne: Cambridge Scholars Pub-
lishing.
Dočekal, Mojmír. 2012a. Atoms, groups and kinds in czech. Acta Linguistica Hungarica
59:109–126.
Dočekal, Mojmír. 2012b. Czech dokud and telicity. In Proceedings of Sinn und Bedeutung
16, ed. Rick Nouwen Ana Aguilar Guevara, Anna Chernilovskaya, 183–197. Boston,
MA: MIT Working Papers in Linguistics.
Dočekal, Mojmír, and Ivona Kučerová. 2009. Bound ability readings of imperfective
verbs: The case for presupposition. Presented at the Formal Aapproaches to Slavic
Linguistics 18, Cornell, NY, May 2009.
Dočekal, Mojmír, and Ivona Kučerová. 2012. Focus on weak islands. A talk presented
at SinFonIJA V, Vienna, Austria.
Dočekal, Mojmír, and Ivona Kučerová. 2013. On the semantics of negative manner and
degree questions: A case study from czech. In FASL 21, ed. Steven Franks. Michigan
Slavic Publications. In press.
61
Bibliography
Dočekal, Mojmír, and Hana Strachoňová. 2012. Negace a skopus kvantifikátorů. A talk
presented at Gramatika a korpus IV, Prague, Czech republic.
Dowty, David. 1979. Word meaning and Montague grammar. Dordrecht: D. Reidel.
Filip, Hana. 1999. Aspect, eventuality types and noun phrase semantics. New York:
Garland Publishing.
Filip, Hana. 2003. Prefixes and the delimitation of events. Journal of Slavic linguistics
11:55–101.
Filip, Hana. 2005. The telicity parameter revisited. In Semantics and Linguistic Theory
XIV , 92–109. Ithaca, NY: Cornell University.
Filip, Hana. 2008. Events and maximalization. In Theoretical and crosslinguistic approaches
to the semantics of Aspect, ed. Susan Rothstein, 217–256. John Benjamins.
Filip, Hana. 2012. Semantics: An international handbook of natural language meaning,
chapter Aspectual class and Aktionsart, 1186–1217. Berlin and New York: Mouton
de Gruyter.
Filip, Hana, and Susan Rothstein. 2006. Telicity as a semantic parameter. In Annual
Workshop on Formal Approaches to Slavic Linguistics, 139–.
von Fintel, Kai. 1999. Npi licensing, strawson entailment, and context dependency.
Journal of Semantics 16:97–148.
von Fintel, Kai. 1994. Restrictions on quantifier domains. Doctoral Dissertation, University
of Massachusetts at Amherst.
Fodor, Janet, and Ivan Sag. 1982. Referential and quantificational indefinites. Linguistics
and Philosophy 5:355–398.
Fox, Danny, and Martin Hackl. 2006. The universal density of measurement. Linguistics
and Philosophy 29:537–586.
Frege, Gottlob. 1892. Über sinn und bedeutung. In Translations from the philosophical
writings of gottlob frege, ed. P. Geach and M. Black. Oxford, Blackwell, third edition.
Gajewski, Jon. 2010. A note on licensing strong npis. University of Connecticut.
van Geenhoven, Veerle. 1998. Semantic incorporation and indefinite descriptions: Semantic
and syntactic aspects of noun incorporation in West Greenlandic. Stanford:
CSLI Publications.
Giannakidou, Anastasia. 2002. Until, aspect and negation: a novel argument for two
untils. In Semantics and Linguistic Theory (SALT) 12, ed. Brendan Jackson, 84–103.
Cornell University, Ithaca, NY: CLC Publications.
62
Bibliography
Grice, Herbert P. 1989. Studies in the ways of words. Harvard University Press.
Hajičová, Eva. 1973. Negation and topic vs. comment. Philologica Pragensia 16:81–93.
Hajičová, Eva. 1974. Negace a presupozice ve významové stavbě věty [Negation and
presupposition in the meaning structure of a sentence]. Prague: Academia.
Hajičová, Eva. 1975. Negace a presupozice ve významové stavbě věty. Praha: Academia.
Heim, Irene. 1994. Interrogative semantics and Karttunen’s semantics for know. In IATL
1, ed. R. Buchalla & A. Mittwoch, 128–144. Jerusalem: Akademon.
Hoeksema, Jack. 1998. In days, weeks, months, years, ages: A class of temporal negativepolarity
items. Rijksuniversiteit Groningen.
Hoeksema, Jack. 1999. Blocking effects and polarity sensitivity. In JFAK. Essays dedicated
to Johan van Benthem on the Occasion of his 50th Birthday. Amsterdam: Vossiuspers/Amsterdam
University Press.
de Hoop, Helen. 1992. Case configuration and noun phrase interpretation. Doctoral
Dissertation, Rijkuniversiteit Groningen.
Horn, Laurence R. 1989. A natural history of negation. University Of Chicago Press.
Hornstein, Norbert. 1990. As time goes by:tense and universal grammar. Bradford
Books and MIT Press.
Iatridou, Sabine, Elena Anagnostopoulou, and Roumyana Izvorski. 2001. Some observations
about the form and meaning of the perfect. In Ken Hale: A Life in Language,
ed. M. Kenstowicz, 189–238. Cambridge, Mass: MIT Press.
Jackendoff, Ray. 1972. Semantic interpretation in generative grammar. Cambridge,
Mass.: MIT Press.
Kadmon, Nirit. 2001. Formal pragmatics. Blackwell Publishing.
Kadmon, Nirit, and Craige Roberts. 1988. Prosody and scope: The role of discourse
structure. In CLS 22, Part 2: Papers from the Parasession on Pragmatics and Grammatical
Theory, ed. P. Farley A. Farley and K-E. McCullough, 16–28. Chicago Linguistic
Society.
Kamp, Hans, and Uwe Reyle. 1993. From discourse to logic. Dordrecht: Kluwer.
Karttunen, Lauri. 1974. Presuppositions and linguistic context. Theoretical Linguistics
1:181–194.
Karttunen, Lauri. 1977. Syntax and semantics of questions. Linguistics and Philosophy
1:3–44.
63
Bibliography
Kiparsky, Paul. 1973. “elsewhere” in phonology. In A festschrift for Morris Halle, ed.
Stephen R. Anderson and Paul Kiparsky, 93–106. New York: Holt, Rinehart and
Winston.
Klein, Wolfgang. 1994. Time in language. New York: Routledge.
Ko, Heejeong. 2007. Asymmetries in scrambling and cyclic linearization. Linguistic
Inquiry 38:49–83.
Kratzer, Angelika. 1998. Scope or pseudo-scope? Are there wide-scope indefinites? In
Events in grammar, ed. S. Rothstein, 163–196. Dordrecht: Kluwer.
Krifka, Manfred. 1989a. Nominal reference, temporal constitution, and quantification
in event semantics. In Semantics and Contextual Expressions, ed. John van Benthem
Renate Bartsch and Peter van Emde Boas, 75–115. Dordrecht: Foris.
Krifka, Manfred. 1989b. Nominalreferenz und zeitkonstitution: Studien zur theoretischen
linguistik. Munchen: Wilhelm Fink.
Krifka, Manfred. 1992. Thematic relations as links between nominal reference and temporal
constitution. In Lexical Matters, ed. Ivan Sag & Anna Szabolcsi, 29–53. Chicago:
CSLI Publications, Chicago University Presss.
Krifka, Manfred. 1999. At least some determiners aren’t determiners. In The Semantics/Pragmatics
Interface from Different Points of View, ed. K. Turner. Amsterdam:
Elsevier.
Kučerová, Ivona. 2012. Grammatical marking of givenness. Natural Language Semantics
1:1–30.
Ladusaw, William A. 1980. Polarity sensitivity as inherent scope relations. Garland
Publishing.
Landman, Fred. 1989. Groups, I. Linguistics and Philosophy 12:559–605.
Landman, Fred. 1997. Plurality. In The handbook of contemporary semantic theory, ed.
Shalom Lappin, 297–322. Blackwell Publishing.
Landman, Fred. 2000. Events and plurality: The Jerusalem lectures. Dordrecht: Kluwer
Academic Publishers.
Landman, Fred. 2004. Indefinites and the type of sets. Oxford: Blackwell.
Landman, Fred. 2011. Boolean pragmatics. Tel Aviv University.
Link, Godehard. 1983. The logical analysis of plurals and mass terms: A latticetheoretical
approach. In Meaning, use and the interpretation of language, ed. Rainer
Bäurle, Christoph Schwarze, and Arnim von Stechow, 303–323. Berlin: Walter de
Gruyter.
64
Bibliography
Löbner, Sebastian. 1995. On one-eyed and two-eyed semantics: Outlines of a theory
of natural language negation and predication. In Blaubeuren Papers: Proceedings of
the Symposium “Recent Developments in Natural Language Semantics" – SfS-report
(working papers of the Seminar für Sprachwissenschaft, Universität Tübingen), ed.
J. Kolb F. Hamm and A. von Stechow. Tübingen.
Longobardi, Giuseppe. 1994. Reference and proper names: A theory of n-movement in
syntax and logical form. Linguistic Inquiry 25:609–655.
Longobardi, Giuseppe. 1996. The syntax of n-raising: A minimalist theory. In OTS
Working Papers. Utrecht: OTS.
Montague, Richard. 1973. The proper treatment of quantification in ordinary english. In
Approaches to Natural Language, ed. Patrick Suppes Jaakko Hintikka, Julius Moravcsik,
221–242. Dordrecht.
Neeleman, Ad, and Kriszta Szendrői. 2007. Radical pro drop and the morphology of
pronouns. Linguistic Inquiry 38:671–714.
Obenauer, Hans-Georg. 1984/1985. On the identification of empty categories. The
Linguistic Review 4:153–202.
Partee, Barbara. 1987. Noun phrase interpretation and type shifting principles. In Studies
in Discourse Representation Theory and the Theory of Generalized Quantifiers,
ed. Dick de Jongh Jeroen Groenendijk and Martin Stokhof. Dordrecht: Kluwer.
Partee, Barbara H., and Mats Rooth. 1983. Generalized conjunction and type ambiquity.
In Meaning, use and the interpretation of language, ed. Christoph Schwarze
Rainer Bäurle and Arnim von Stechow. Walter de Gruyter & Co.
Penka, Doris. 2007. Negative indefinites. Doctoral Dissertation, Universität Tübingen.
Pesetsky, David. 1987. Wh-in-situ: Movement and unselective binding. In The representation
of (in)definitess, ed. E. Reuland and A. ter Meulen, 98–129. Cambridge: MIT
Press.
Petr, Jan, Miloš Dokulil, Karel Horálek, Jiřina Hůrková, and Miloslava Knappová, ed.
1986. Mluvnice češtiny [Grammar of Czech]. Praha: Academia.
Pollock, Jean-Yves. 1989. Verb movement, universal grammar, and the structure of IP.
Linguistic Inquiry 20:365–424.
Portner, Paul H. 2005. What is meaning? fundamentals of formal semantics. Blackwell
Publishing.
Reichenbach, Hans. 1947. Elements of symbolic logic. London: Collier-MacMaillan.
Reinhart, Tanya. 1997. Quantifier scope: How labor is divided between QR and choice
functions. Linguistics and philosophy 20:335–397.
65
Bibliography
Roberts, Craige. 1987. Modal subordination and distributivity. Doctoral Dissertation,
UMass, Amherst. Published 1990, Garland, New York.
Rooth, Mats. 1992a. A theory of focus interpretation. Natural Language Semantics
1:75–116.
Rothstein, Susan. 2004. Structuring events: A study in the semantics of lexical aspect.
Oxford: Blackwell Publishing.
Rothstein, Susan. 2008. Telicity and atomicity. In Theoretical and Crosslinguistic Approaches
to the Semantics of Aspect, ed. S. Rothstein, 43–78. Amsterdam: John Ben-
jamins.
Rullmann, Hotze. 1995. Maximality in the semantics of Wh-constructions. Doctoral
Dissertation, University of Massachusetts at Amherst.
Russell, Bertrand. 1905. On denoting. Mind 14:479–493.
Sauerland, Uli. 2003. A new semantics for number. In Proceedings of SALT 13, ed.
R. Young and Y. Zhou. Cornell University, Ithaca, NY: CLC Publications.
Scha, Remko. 1981. Distributive, collective and cumulative quantification. In Truth,
Interpretation, Information, ed. T. Janssen J. Groenendijk and M. Stokhof. Dordrecht:
Foris.
Schein, Barry. 1993. Plurals and events. Cambridge, Mass.: MIT Press.
Schwarz, Bernhard, and Junko Shimoyama. 2011. Negative islands and obviation by
‘wa’ in Japanese degree questions. In Proceedings of SALT, volume 20, 702–719.
Schwarzschild, Roger. 1994. Plurals, presuppositions and the sources of distributivity.
Natural Language Semantics 2:201–248.
Schwarzschild, Roger. 1996. Pluralities. Springer.
von Stechow, Arnim. 2002. German seit ’since’ and the ambiguity of german perfect. In
More than words. A Festscrhift für Dieter Wunderlich, ed. Ingrid Kaufman & Barbara
Stiebels, 393–432. Berlin: Akademie Verlag.
von Stechow, Arnim. 2009. The expression time in language, chapter Tenses in Compositional
Semantics. To appear.
de Swart, Henriette. 1996. Meaning and use of not ...until. Journal of Semantics
13:221–263.
Szabolcsi, Anna. 2006. The blackwell companion to syntax, chapter Strong vs. weak
islands, 479–532. Blackwell.
66
Bibliography
Szabolcsi, Anna, and Bill Haddican. 2004. Conjunction meets negation: a study in
crosslinguistic variation. Journal of Semantics 21:219–249.
Szabolcsi, Anna, and Frans Zwarts. 1993. Weak islands and an algebraic semantics for
scope taking. Natural Language Semantics 1:235–284.
Vendler, Zeno. 1957. Verbs and times. The Philosophical Review 66:143–160.
Verkuyl, Henk. 1993. A theory of aspectuality. Cambridge: Cambridge Univ Press.
Winter, Yoad. 2001. Flexibility principles in boolean semantics: coordination, plurality
and scope in natural language. Cambridge, Mass.: MIT Press.
Winter, Yoad. 2005. On some problem of (in)definiteness within flexible semantics.
Lingua 115:767–786.
Zeijlstra, Hede. 2004. Sentential negation and negative concord. Doctoral Dissertation,
University of Amsterdam, Amsterdam.
Zimmermann, Edde. 1993. On the proper treatment of opacity in certain verbs. Natural
Language Semantics 1.
67