Spring 2012
Juyeon Kang
qkang@fi.muni.cz
B410, Faculty of Informatics, Masaryk University,
Brno, Czech Rep.
IA165
Combinatory Logic for
Computational Semantics
2
PART I
● General Information about the course
on ”CL for CS”
3
● 12 lectures + 1 revision session from 24.02.2012 to
18.05.2012
● Class composition: lecture (1h) + classwork (45h)
● Friday from 12h to 1:50p.m
● Evaluation:
Homework (30%) + Final exam. (50%) + Attendance (10%)
+ Participation (10%)
● Contact teacher: qkang@fi.muni.cz office: B206
● Course web page:
https://is.muni.cz/auth/course/fi/spring2012/IA165
4
Objectives
● Introduce the Combinatory Logic and its application to Computational
Semantics
: How the CL can be applied to semantic analysis of natural language
● Be familiar with a practical technique of constructing semantic
representations of natural language and discover the properties of
natural language
5
Main readings
● H. Curry and R. Fey, Combinatory Logic, Vol1&2, 1958.
● P. Blackburn and Johan Bos, Representation and Inference
for Natural Languages: A First Course in Computational
Semantics, CSLI Publications, 2005.
● J.R. Hindley and J.P. Seldin, λ-calculus and Combinators: An
introduction. Cambridge Univ. Press.
6
PART II
Background on Computational Semantics
7
Why the Computational Semantics?
● Promising approach for many domain-embedded
applications is to use the benefits of statistical
models for disambiguation at a lexical/syntactic
level, and then to use logical semantic
representations for detailed interpretations
8
Overview on Formal semantics
Artificial Intelligence
Artificial Intelligence
Syntax
Syntax
Landscape from M. Kohlhase's working paper (2010)
World
knowledge
Semantic/
pragmatic
analysis
Inference
Lexicon
Lexical
Semantics
Semantic
composition
Lexicon
Discourse
9
Traditional Topics of CS
● Construction of meaning representation
● Semantic underspecification
● Anaphora resolution
● Presupposition projection
● quantifier scope resolution-formal semantics
● Statistical semantics
→ point of contact with lexical semantics
word sense disambiguation, semantic role labeling
10
What to do
● How can we automate the process of associating
semantic representations with expressions of natural
language?
Language MeaningRepresentation
11
Logical tools used in builiding meaning
representation
● Use of First-Order Logic
● Use of Lamda-Calculus
● Use of Combinatory Logic
● Use of Type Theory
● Use of Propositional Logic
● Use f Modal Logic
● Various dynamic approaches (DRT, DPL...)
→ translating such simple sentences as ”John loves Mary” and ”A woman
walks” into formal semantic representations being→ systematic
12
Building a Semantic representation
● We need to complete he next three steps:
step 1: specify the reasonable syntax for the natural language fragment
of interest
step 2 Specify semantic representations for the lexical items.
step 3 Specify the translation of constituents compositionally.
∀x(MAN(X) → WALK(x) in first-order formula
(λx.love(x, mary))(john) ⇒ love(john, mary) in lambda term
13
What we mean by ”systematic”
● In First-Order Logic,
John loves Mary
Semantic content is captured by the first-order formula :
LOVE(JOHN, MARY)
abstract denotation
14
How to be systematic
● Notion of syntactic structure
John loves Mary (S)
LOVE(JOHN, MARY)
John (NP) loves Mary (VP)
JOHN LOVE (?, MARY)
loves (TV) MARY (NP)
LOVE (?,?) MARY
15
Summing up
● Building meaning representation
1)lexical items
2)syntactic structure
3)from syntax to semantics
→ tell us how the semantic constructions of the parts of a sentence are
to be joined together.
16
Syntax-semantic interface
● How to build a complete first-order formula?
- The mecanism we're can mention is λ−calculus.
That is, lambda calculus is viewed as a notational extension of firstorder
logic : new operator for binding variables → λ
ex: simple λ−expression
λx.woman(x)
17
Function -argument structure
« A function is a rule of correspondence by which when anything is given
(as argument) another thing (the value of the function for that
argument) may be obtained. That is, a function is an operation which
may be applied on one thing (the argument) to yield another thing (the
value of the function)... »
-A.Church (1941)
18
Concepts for Functional application
vs.
#Non chronological order
• Incomplete expression theory of Frege (1879)
• ”Logische Untersuchungen” (the distinction between dependent expression
and independent expression) of Husserl (1900)
● operator
● Function
● Syncategoreme
● Incomplete expression
● operator
● Function
● Syncategoreme
● Incomplete expression
● operand
● Argument
● Categoreme
● Complete expression
● operand
● Argument
● Categoreme
● Complete expression
19
● All linguistic expression are viewed as operators or operands.
Conventional notation: (operator(operand))
operator
operator
operand
operand
@
Verbes, adverbes,
prepositions, conjonctors,
negation, punctuation...
Noun phrase, Sentence
20
● One example: John eats an icecream
eats an icecream John
@
@
@ (an (icecream))
(eats(an (icecream)))
((eats(an (icecream)))John)
S
NP VP
PN TV NP
DET N
John Eats an icecream
21
Computing semantic
representation
● How do we automate the process of assigining semantic representations
to sentences of human language?
Human
languagesentences
Semantic
represenction
Input Output
22
● Two main approaches
1) use of the unification
2) use of the lambda calculus
→ They both requires a grammar describing the syntactic structure of
the fragment of language of interest.
23
∃x(WOMAN(x)∧WALK(x))∃x(WOMAN(x)∧WALK(x))
24
Semantic construction system
● One example of a modular implementation of a semantic construction
system by Burchardt, Koller and Walter
S sSem(λp.p(john)@λx.walk(x))
NP VP npSem(λp.p(john)) vpSem(λx.walk(x))
PN IV pnSem(λp.p(john)) ivSem(λx.walk(x))
John walks
lexicon
lexicon
Combine with
Semantic Macros
Semantic Macros
DCG
25
● Various ways to construct logical formulae as meaning representations
for sentences
→ How to do useful work with such meaning representation?
Finding out what can be inferred
from the formula constructed for a sentence
is a very important task in Computation Semantics.
Finding out what can be inferred
from the formula constructed for a sentence
is a very important task in Computation Semantics.
26
Next week...
● We will view the Combinatory Logic as a logical tool for
representing a semantic meaning.