combinatory categorial grammar (ccg)
TRANSCRIPT
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Combinatory Categorial Grammar (CCG)
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Categories
Categories = types
Primitive categories
N, NP, S, PP, etc
Functions
a combination of primitive categories
S/NP, (S/NP) / (S/NP), etc
V, VP, Adverb, PP, etc
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Combinatory Rules
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z forward crossing composition: x/y y\z x\z backward crossing composition: x\y y/z x/z
Type-raising forward type-raising: x y / (y\x)
backward type-raising: x y \ (y/x)
Coordination <&> x conj x x
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Combinatory Rules 1 : Application Forward application “>”
X/Y Y X
(S\NP) / NP NP S\NP
Backward application “<“
Y X\Y X
NP S\NP S
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Function likes := (S\NP) / NP
A transitive verb is a function from NPs into predicate S. That is, it accepts two NPs as arguments and results in S.
VP or intransitive verb: S\NP
Transitive verb: (S\NP) / NP
Adverb: (S\NP) \ (S\NP)
PP: ((S\NP) \ (S\NP)) / NP
(NP\NP) / NP
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CCG Derivation:
CFG Derivation:
Examples from Prof. Julia Hockenmaier
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Combinatory Rules
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z forward crossing composition: x/y y\z x\z backward crossing composition: x\y y/z x/z
Type-raising forward type-raising: x y / (y\x)
backward type-raising: x y \ (y/x)
Coordination <&> x conj x x
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Combinatory Rules 4 : Coordination X conj X X
Alternatively, we can express coordination by defining conjunctions as functions as follows:
and := (X\X) / X
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Coordination with CCG
Examples from Prof. Mark Steedman
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Coordination with CCG
Application
forward application: x/y y x
backward application: y x\y x
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Coordination with CCG
Application
forward application: x/y y x
backward application: y x\y x
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Combinatory Rules
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z forward crossing composition: x/y y\z x\z backward crossing composition: x\y y/z x/z
Type-raising forward type-raising: x y / (y\x)
backward type-raising: x y \ (y/x)
Coordination <&> x conj x x
![Page 13: Combinatory Categorial Grammar (CCG)](https://reader031.vdocuments.site/reader031/viewer/2022020705/61fb8c852e268c58cd5f7d0f/html5/thumbnails/13.jpg)
Coordination with CCG
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z
forward crossing composition: x/y y\z x\z
backward crossing composition: x\y y/z x/z
![Page 14: Combinatory Categorial Grammar (CCG)](https://reader031.vdocuments.site/reader031/viewer/2022020705/61fb8c852e268c58cd5f7d0f/html5/thumbnails/14.jpg)
Coordination with CCG
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z
forward crossing composition: x/y y\z x\z
backward crossing composition: x\y y/z x/z
![Page 15: Combinatory Categorial Grammar (CCG)](https://reader031.vdocuments.site/reader031/viewer/2022020705/61fb8c852e268c58cd5f7d0f/html5/thumbnails/15.jpg)
Combinatory Rules
Application forward application: x/y y x
backward application: y x\y x
Composition forward composition: x/y y/z x/z
backward composition: x\y y\z x\z forward crossing composition: x/y y\z x\z backward crossing composition: x\y y/z x/z
Type-raising forward type-raising: x y / (y\x)
backward type-raising: x y \ (y/x)
Coordination <&> x conj x x
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Combinatory Rules 3 : Type-Raising Turns an argument into a function
Forward type-raising: X T / (T\X)
Backward type-raising: X T \ (T/X)
For instance…
Subject type-raising: NP S / (S \ NP)
Object type-raising: NP (S\NP) \ ((S\NP) / NP)
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Combinatory Rules 3 : Type-Raising
Application forward application: x/y y x
backward application: y x\y x
Type-raising forward type-raising: x y / (y\x)
backward type-raising: x y \ (y/x)
Subject type-raising: NP S / (S \ NP)
Object type-raising: NP (S\NP) \ ((S\NP) / NP)
Coordination <&> x conj x x
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Combinatory Rules 3 : Type-Raising
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Tree Adjoining Grammar (TAG)
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Some slides are from Prof. Julia Hockenmaier
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TAG rule 1: Substitution
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TAG rule 2: Adjunction
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The effect of adjunction
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Example: TAG Lexicon
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Example: TAG Derivation
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Example: TAG Derivation
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Example: TAG Derivation
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Cross-serial Dependencies
Dutch and Swiss-German
Comparison to regular grammar and CFG?
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