Spring 2012
Juyeon Kang
qkang@fi.muni.cz
B410, Faculty of Informatics, Masaryk University,
Brno, Czech Rep.
IA165
Combinatory Logic for
Computational Semantics
Summing up: last lecture
● How to apply the combinators to natural language analysis
1) using introduction and elimination rules by beta-reduction of
combinators: control heurstic of combinatorial application and bracketing
2) using a syntactic tool for controlling the application of combinators
: CCG assumes the preliminary steps to find a well-structured normal
form, that is, a formal semantic structure
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Coordination (Φ)
x:e1  CONJ  x:e2
­­­­­­­­­­­­­­­­­> (> )Φ
x:   CONJ e1 e2 Φ
e1 of type x coordinated with e2 of type x by the conjonction 'and'
 
(S\NP)/NP:pick    CONJ:'and'    (S\NP)/NP:eat
       ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­> (>Φ)
(S\NP)/NP:   Φ and pick eat
e1 of type x coordinated with e2 of type x by the conjonction 'and'
 
(S\NP)/NP:pick    CONJ:'and'    (S\NP)/NP:eat
       ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­> (>Φ)
(S\NP)/NP:   Φ and pick eat
Remind 1...
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Extraction asymmetries
1. subject-object asymmetry
2. NP shifted arguement
3. type-raised argument
4. leftward extraction of ”non-peripheral argument”
==> Such asymmetries exist in SVO languages because of the possibility of
”scrambling” arguments across clause boundaries.
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1. subject-object asymmetry of English
(1) *Brazil is the team_i that John knew that t_i would beat Germany.
(2) Germany is the team_i that John knew that Brazil would beat t_i.
Comment: We see in (1) that extraction of the subject from the
embedded clause to form the relative clause is ungrammatical,
whereas the object is accessible for extraction, as shown in (2).
Unlike the situation with many island violations, there is nothing
semantically incoherent about a relative clause such as that in (1),
and the grammar apparently disallows it for entirely syntactic
reasons.
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2. NP shifted arguement
(1) I shall buy today and cook tomorrow the mushrooms
         (1’) I shall buy the mushrooms today
         (1’’) I shall cook the mushrooms tomorrow
CONJ:
and
CONJ:
and
(Shall and ((today (buy (the mushrooms))) ((tomorrow (cook 
(the mushrooms))) I)
Semantic classes of adv:
speech-act modifier(peripheral: core as argument), subjectoriented
modifier, sentence modifier, VP modifier (nonperipheral:
subparts as argument), ...
Semantic classes of adv:
speech-act modifier(peripheral: core as argument), subjectoriented
modifier, sentence modifier, VP modifier (nonperipheral:
subparts as argument), ...
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3. type-raised argument
(1) I will give to my sister an engraving by Rambrandt
The complement object (NPobj) ”to my sister” is type-raised.
To + NPobj= PP as derteminant of verb give
Type­raising rule with C*
X:e1(=NPobj)
­­­­­­­­­­­­­­<C*
y\(y/x): C*e1
y is a variable over categories, ranging 
over the result types of functions over x.
Type­raising rule with C*
X:e1(=NPobj)
­­­­­­­­­­­­­­<C*
y\(y/x): C*e1
y is a variable over categories, ranging 
over the result types of functions over x.
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4. leftward extraction of ”non-peripheral argument”
● Cases of non-peripheral extraction
(1) (articles) which I will file tomorrow
(1’) I will file the articles tomorrow
(2) an engraving which I will buy today and sell tomorrow
(2’) I will buy (an engraving) today and sell an engraving tomorrow
(3) an engraving which I will show to him and give to you
(3’) I will show an engraving to him and give an engraving to you 
Such non-peripheral extraction is often done with a permutation
operator and the introduction of the permutation operator increases
the power.
Such non-peripheral extraction is often done with a permutation
operator and the introduction of the permutation operator increases
the power.
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Non-order-preserving composition
Backward crossed composition rule with the combinator B (<Bx)
Y/Z X\Y   =>  X/Z  (<Bx)
Y/Z:e1  X\Y:e2
­­­­­­­­­­­­­­< (Bx)
x/z: B e2 e1
allows to consider heavy NP shift and related coordinationallows to consider heavy NP shift and related coordination
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Extraction aymmetries analyzed in terms of the
combinators-1
1. subject-object asymmetry of English
(1) Germany is the team_i that John knew that Brazil would beat t_i.
1/ NP:Germany (S\NP)/NP:is NP:the team ((NP\NP)/S):that NP:John 
(S\NP)/NP:knew (NP/(S/NP)):that NP:Brazil ((S\NP)/NP)/((S\NP)/NP):would 
(S\NP)/NP:beat  
2/ S/(S\NP):(C* Germany) (S\NP)/NP:is NP:the team ((NP\NP)/S):that S/
(S\NP):C*John (S\NP)/NP:knew (NP/(S/NP)):that S/(S\NP):(C* Brazil) 
((S\NP)/NP)/((S\NP)/NP):would (S\NP)/NP:beat   (>C*)
3/ S/NP: B(C* Germany) is
4/ ((NP\NP)/S):that S/(S\NP):C*John (S\NP)/NP:knew (NP/(S/NP)):that S/
(S\NP):C*Brazil ((S\NP)/NP):would beat
5/  ((NP\NP)/S):that S/NP:(B(C*John)knew) (NP/(S/NP)):that S/NP: (B(C*Brazil) 
would beat)
6/   ((NP\NP)/S):that S/NP:(B(C*John)knew) NP:(that (B(C*Brazil) would beat))
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6/   ((NP\NP)/S):that S/NP:(B(C*John)knew) NP:(that (B(C*Brazil) would 
beat))
7/ ((NP\NP)/S):that S:((B(C*John)knew)(that (B(C*Brazil) would beat)))
8/ (NP\NP):(that((B(C*John)knew)(that (B(C*Brazil) would beat))))
9/NP:(((NP\NP):(that((B(C*John)knew)(that (B(C*Brazil) would beat)))))the 
team)
10/(that((C*John)(knew(that (B(C*Brazil) would beat))))))the team)
11/(that((knew(that (C*Brazil)( would beat)))))(John))the team)
12/(that((knew(that(would beat)(Brazil)))))(John))the team)
Germany is the team that John knew that Brazil would beat
(that((knew(that(would beat)(Brazil)))))(John))
the team)
Germany is the team that John knew that Brazil would beat
(that((knew(that(would beat)(Brazil)))))(John))
the team)
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Extraction aymmetries analyzed in terms of the
combinators-2
2. NP shifted arguement
(1) I buy today and cook tomorrow the mushrooms
VP=(S\NP)
1/NP:I VP/NP:buy VP\VP:today CONJ:and VP/NP:cook VP\VP:tomorrow NP: 
the mushrooms
2/S/(S\NP):C*I
3/ VP/NP:(Bx today buy) CONJ:and VP/NP:(Bx tomorrow cook) (<Bx)
4/ VP/NP:   Φ and (Bx today buy) (Bx tomorrow cook)
5/ S/NP:(B(C*I)(  Φ and (Bx today buy) (Bx tomorrow cook)))
6/ S:(B(C*I)(  Φ and (Bx today buy) (Bx tomorrow cook)))(the 
mushrooms)
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6/ S:(B(C*I)(  Φ and (Bx today buy) (Bx tomorrow cook)))
(the mushrooms)
7/ (C*I)((  Φ and (Bx today buy) (Bx tomorrow cook))(the 
mushrooms))
8/ ((  Φ and (Bx today buy) (Bx tomorrow cook))(the 
mushrooms))(I)
9/ (and ((Bx today buy)(the mushrooms)) ((Bx tomorrow 
cook)(the mushrooms)))(I)
10/ (and (today (buy(the mushrooms))) (tomorrow 
(cook(the mushrooms))))(I)
I buy today and cook tomorrow the mushrooms
(and (today (buy(the mushrooms)))
(tomorrow (cook(the mushrooms))))(I)
I buy today and cook tomorrow the mushrooms
(and (today (buy(the mushrooms)))
(tomorrow (cook(the mushrooms))))(I)
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Extraction aymmetries analyzed in terms of the
combinators-3
3. type-raised argument
(1) I will give (to my sister) an engraving by Rambrandt
VP=(S\NP)
1/ S/VP:C*I VP/VP:will (VP/PP)/NP:give  (VP\(VP/PP)):(C*to my sister) 
NP/N:an N:engraving (N\N)/NP: by  NP: Rambrandt      (<C*)    
2/ S/VP:B((C*I) will) (VP/PP)/NP:give (VP\(VP/PP)):(to(my sister)) 
NP:(an((by Rambrandt) engraving))    (>B)
3/ S/VP:B((C*I) will) (VP/NP):(Bx(to(my sister))give)  NP:(an((by 
Rambrandt) engraving))   (>Bx)
4/ (S/VP):B((C*I) will) VP:((Bx(to(my sister))give)(an((by Rambrandt) 
engraving)))   (>)
5/ S:(B((C*I) will)((Bx(to(my sister))give)(an((by Rambrandt) 
engraving))))   (>)
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5/ S:(B((C*I) will)((Bx(to(my sister))give)(an((by Rambrandt) 
engraving))))   (>)
6/ ((C*I)( will((Bx(to(my sister))give)(an((by Rambrandt) 
engraving))))) (e.B) 
7/(( will((Bx(to(my sister))give)(an((by Rambrandt) engraving))))
(I)) (e.C*) 
8/ (( will(to(my sister)(give(an((by Rambrandt) engraving)))))(I))
(e.B) 
I will give to my sister an engraving by Rambrandt
(( will(to(my sister)(give(an((by Rambrandt) engraving)))))(I))
I will give to my sister an engraving by Rambrandt
(( will(to(my sister)(give(an((by Rambrandt) engraving)))))(I))
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Extraction aymmetries analyzed in terms of the
combinators-4
4. leftward extraction of ”non-peripheral argument”
(1) (articles) which I will file tomorrow
VP=(S\NP)
1/ N: articles (N\N)/(S/NP):which  (S/(S\NP)):(C*I) (VP/VP):will 
VP/NP:file VP\VP:tomorrow
2/ N: articles (N\N)/(S/NP):which  (S/VP):(B(C*I)will) (VP/NP):file 
VP\VP:tomorrow
3/ N: articles (N\N)/(S/NP):which  (S/VP):(B(C*I)will) (VP/NP):(Bx 
tomorrow file)           (<Bx)
4/ N: articles (N\N)/(S/NP):which  (S/NP):B((B(C*I)will)(Bx tomorrow 
file))                    (>B)
5/ N: articles (N\N):which (B((B(C*I)will)(Bx tomorrow file)))    (>)
6/ N: (which (B((B(C*I)will)(Bx tomorrow file))) articles)    (<)
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6/ N: (which (B((B(C*I)will)(Bx tomorrow file))) articles)    (<)
7/(which ((B(C*I)will)(Bx tomorrow file)) articles))   (e­B)
8/ (which ((C*I)(will(Bx tomorrow file)) articles)))   (e­B)
9/ (which (will(Bx tomorrow file)) articles))(I))   (e­C*)
10/ (which (will(tomorrow ((file)articles)))(I))    (e­Bx)
articles which I will file tomorrow
(which(will(tomorrow((file)articles)))(I))
articles which I will file tomorrow
(which(will(tomorrow((file)articles)))(I))
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Next week...
● Continue about the application of the combinators to natural
language analysis: surbodination with ccg tools and passivisation
without CCG tools