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Introduction Learning by Inference Rules Experiment Conclusion

An Inference-rules based Categorial GrammarLearner for Simulating Language Acquisition

Xuchen Yao, Jianqiang Ma, Sergio Duarte, Çağrı Çöltekin

University of Groningen

18 May 2009

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Categorial Grammar

• basic categories: S(sentence), NP (nounphrase), N (noun)

• Complex categories:NP/N, S\NP and(S\NP)\(S\NP)

• Slash operators: / \

Peter saw a bookNP VP DT N

NPVP

SPeter saw a book

NP (S\NP)/NP NP/N N>

NP>

S\NP<

S

Figure: Example derivation forsentence Peter saw a book.

Introduction Learning by Inference Rules Experiment Conclusion

Categorial Grammar

• basic categories: S(sentence), NP (nounphrase), N (noun)

• Complex categories:NP/N, S\NP and(S\NP)\(S\NP)

• Slash operators: / \

Peter saw a bookNP VP DT N

NPVP

SPeter saw a book

NP (S\NP)/NP NP/N N>

NP>

S\NP<

S

Figure: Example derivation forsentence Peter saw a book.

Introduction Learning by Inference Rules Experiment Conclusion

Different Operation Rules

• Function application rules (CG)Forward A/B B → A (>)Backward B A\B → A (<)

• Function composition rules (CCG)Forward A/B B/C → A/C (> B)Backward B\C A\B → A\C (< B)

• Type raising rules (CCG)Forward A → T/(T\A) (> T)Backward A → T\(T/A) (< T)

• Substitution rules (CCG)Forward (A/B)/C B/C → A/C (>S)Backward B\C (A\B)\C → A\C (<S)

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Nativist vs. Empiricist• Auxiliary Verb Fronting

• Peter is awake.• Is Peter awake?• Peter who is sleepy is awake.

• Is Peter who is sleepy awake?• *Is Peter who sleepy is awake?

• Word Order• I should go.• I have gone.• I am going.• I have been going.• I should have gone.• I should be going.

• I should have been going.• *I have should been going.

Introduction Learning by Inference Rules Experiment Conclusion

Nativist vs. Empiricist• Auxiliary Verb Fronting

• Peter is awake.• Is Peter awake?• Peter who is sleepy is awake.

• Is Peter who is sleepy awake?• *Is Peter who sleepy is awake?

• Word Order• I should go.• I have gone.• I am going.• I have been going.• I should have gone.• I should be going.

• I should have been going.• *I have should been going.

Introduction Learning by Inference Rules Experiment Conclusion

Nativist vs. Empiricist• Auxiliary Verb Fronting

• Peter is awake.• Is Peter awake?• Peter who is sleepy is awake.

• Is Peter who is sleepy awake?• *Is Peter who sleepy is awake?

• Word Order• I should go.• I have gone.• I am going.• I have been going.• I should have gone.• I should be going.

• I should have been going.• *I have should been going.

Introduction Learning by Inference Rules Experiment Conclusion

Nativist vs. Empiricist• Auxiliary Verb Fronting

• Peter is awake.• Is Peter awake?• Peter who is sleepy is awake.

• Is Peter who is sleepy awake?• *Is Peter who sleepy is awake?

• Word Order• I should go.• I have gone.• I am going.• I have been going.• I should have gone.• I should be going.

• I should have been going.• *I have should been going.

Introduction Learning by Inference Rules Experiment Conclusion

Research Questions

1. Can we give a computational simulation of the acquisition ofsyntactic structures?

• How do we derive the category of an unknown word in asentence?

2. Can we give a judgement of the Nativist-Empiricist debatefrom the perspective of CCG?

• How important is experience? Or the innate ability is moreimportant?

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Level 0/1 Inference Rules

• Level 0 inference rulesB/A X → B ⇒ X = A ifA 6= SX B\A → B ⇒ X = A ifA 6= S

• Level 1 inference rulesA X → B ⇒ X = B\A ifA 6= SX A → B ⇒ X = B/A ifA 6= S

Peter worksNP X

(S\NP)<

S

Figure: Example of level 1 indefrence rules: Peter works.

Introduction Learning by Inference Rules Experiment Conclusion

Level 2 Inference Rules• Level 2 side inference rules

X A B → C ⇒ X = (C/B)/AA B X → C ⇒ X = (C\A)\B

• Level 2 middle inference ruleA X B → C ⇒ X = (C\A)/B

Peter saw a book

NP X NP/N N((S\NP)/NP)

>

NP>

S\NP<

S

Figure: Example of level 2 inference rules: Peter saw a book.

Introduction Learning by Inference Rules Experiment Conclusion

Level 3 Inference Rules

• Level 3 side inference rulesX A B C → D ⇒ X = ((D/C )/B)/AA B C X → D ⇒ X = ((D\A)\B)\C

• Level 3 middle inference rulesA X B C → D ⇒ X = ((D\A)/C )/BA B X C → D ⇒ X = ((D\A)\B)/C

• Inference rules of up to level 3 can derive most categories ofcommon English words.

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

The Learning Architecture

CorpusEdge

GeneratorRecursiveLearner

Level 0IR canparse?

Level 1IR canparse?

Level 2IR canparse?

Level 3IR canparse?

NN NN

Applying level 0 and 1 inference

rule recursively

SCP Principle

Rightcombining

rule

Output SelectorY

Generationrule set

Testrule set

Cannot learn

NN

YY YYYYYY

Figure: Learning process using inference rules

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Target Grammar

Peter := NP with := (N\N)/NPMary := NP with := (NP\NP)/NPbig := N/N with := ((S\NP)\(S\NP))/NPcolorless := N/N sleep := S\NPbook := N a := NP/Ntelescope := N give := ((S\NP)/NP)/NPthe := NP/N saw := (S\NP)/NPrun := S\NP read := (S\NP)/NPbig := N/N furiously := (S\NP)\(S\NP)

Table: Target Grammar Rules

• Recursive & ambiguous• Assume only NP and N are known to the learner

Introduction Learning by Inference Rules Experiment Conclusion

Result

Peter saw Mary with a big big telescope

NP (S\NP)/NP NP (NP\NP)/NP NP/N N/N N/N N>

N>

N<

NP>

NP\NP<

NP>

S\NP<

S

(a)

Peter saw Mary with a big big telescope

NP (S\NP)/NP NP ((S\NP)\(S\NP))/NP NP/N N/N N/N N> >

S\NP N>

N<

NP>

(S\NP)\(S\NP)<

S\NP<

S

(b)

Figure: Two ambiguous parses of the sentence

Introduction Learning by Inference Rules Experiment Conclusion

Result

Peter saw Mary with a big big telescope

NP (S\NP)/NP NP (NP\NP)/NP NP/N N/N N/N N>

N>

N<

NP>

NP\NP<

NP>

S\NP<

S

Figure: Ambiguous parse 1

Introduction Learning by Inference Rules Experiment Conclusion

Result

Peter saw Mary with a big big telescope

NP (S\NP)/NP NP ((S\NP)\(S\NP))/NP NP/N N/N N/N N> >

S\NP N>

N<

NP>

(S\NP)\(S\NP)<

S\NP<

S

Figure: Ambiguous parse 2

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Learning Auxiliary Verb Fronting 1

Peter is sleepy

NP (S\NP)/(Sadj\NP) Sadj\NP>

S\NP<

S(a)

Is Peter awake

(Sq/(Sadj\NP))/NP NP Sadj\NP>

Sq/(Sadj\NP)<

Sq(b)

Peter who is sleepy is awake

NP (NP\NP)/(S\NP) (S\NP)/(Sadj\NP) Sadj\NP (S\NP)/(Sadj\NP) Sadj\NP> >

S\NP S\NP>

NP\NP<

NP<

S(c)

Figure: Learning Auxiliary Verb Fronting 1

Introduction Learning by Inference Rules Experiment Conclusion

Learning Auxiliary Verb Fronting 2

Is Peter who is sleepy awake

(Sq/(Sadj\NP))/NP NP (NP\NP)/(S\NP) (S\NP)/(Sadj\NP) Sadj\NP Sadj\NP>

S\NP>

NP\NP<

NP>

Sq/(Sadj\NP)>

Sq

Figure: Learning Auxiliary Verb Fronting 2

• is := (S\NP)/(Sadj\NP)Is := (Sq/(Sadj\NP))/NP

Introduction Learning by Inference Rules Experiment Conclusion

Outline

IntroductionCombinatory Categorial GrammarLanguage Acquisition

Learning by Inference RulesGrammar Induction by Inference RulesThe Learning Architecture

ExperimentLearning an Artificial GrammarLearning Auxiliary Verb FrontingLearning Correct Word Order

Conclusion

Introduction Learning by Inference Rules Experiment Conclusion

Learning Correct Word Order• I should go.• I have gone.• I am going.• I have been going.• I should have gone.• I should be going.• I should have been going.• *I have should been going.

should := (Ss\NP)/(S\NP)should := (Ss\NP)/(Sh\NP)should := (Ss\NP)/(Sb\NP)have := (Sh\NP)/(S\NP)have := (Sh\NP)/(Sb\NP)be := (Sb\NP)/(S\NP)

I should have been going

NP (Ss\NP)/(Sh\NP) (Sh\NP)/(Sb\NP) (Sb\NP)/(S\NP) S\NP>

Sb\NP>

Sh\NP>

Ss\NP<

Ss

Figure: Learning Correct Word Order

Introduction Learning by Inference Rules Experiment Conclusion

Conclusion

1. Can we give a computational simulation of the acquisition ofsyntactic structures?

• How do we derive the category of an unknown word in asentence?

• This paper presents a simple and intuitive method to achievethis.

2. Can we give a judgement of the Nativist-Empiricist debatefrom the perspective of CCG?

• How important is experience? Or the innate ability is moreimportant?

• Simple and intuitive logical rules can also help resolve thecelebrated linguistic phenomena.

• Logic gives a third way beside experience and innateness.

Introduction Learning by Inference Rules Experiment Conclusion

Conclusion

1. Can we give a computational simulation of the acquisition ofsyntactic structures?

• How do we derive the category of an unknown word in asentence?

• This paper presents a simple and intuitive method to achievethis.

2. Can we give a judgement of the Nativist-Empiricist debatefrom the perspective of CCG?

• How important is experience? Or the innate ability is moreimportant?

• Simple and intuitive logical rules can also help resolve thecelebrated linguistic phenomena.

• Logic gives a third way beside experience and innateness.