The Syntax-Semantics Interface: Theory and … · 1 1 A Brief Overview of Glue Semantics and Linear...

The Syntax-Semantics Interface: Theory and ImplementationAsh Asudeh: http://www.stanford.edu/˜asudeh/Dick Crouch: http://www.parc.com/istl/members/crouch/Mary Dalrymple: http://www.parc.com/istl/members/dalrymple/NASSLLI’02, M-F 1:30-2:30http://www.stanford.edu/group/nasslli/courses/Glue.htm

This course introduces issues in the syntax-semantics interface from a theoretical and implementational perspective,centered on the topics of resource management, modification, quantification, and ellipsis. The theory introducedis Glue Semantics (GLUE), which uses linear logic to perform semantic composition through deduction on logicalpremises obtained from syntactic analysis. The syntactic theory we assume is Lexical Functional Grammar (LFG),although there will be some discussion of how GLUE can be integrated into other syntactic frameworks. No priorknowledge of GLUE or LFG is assumed: the first portion of the class introduces GLUE and LFG, motivates GLUE asa theory of the syntax-semantics interface, and compares this theory to other current theories.

Prerequisites: Introductory syntax and semantics

1 Timetable

Monday, 24 June General introduction; introduction to linear logic/proof theoryRecommended readings: Dalrymple et al. (1995), Crouch and van Genabith (2000)

Tuesday, 25 June Introduction to LFG, GLUE; some simple sentences; modificationRecommended readings: Wescoat (1989), Dalrymple (2001, Chapters 2, 9, 10)

Wednesday, 26 June Quantification, ellipsisRecommended readings: Dalrymple (2001, Chapter 9), Asudeh and Crouch (2002a)

Thursday, 27 June Issues in resource managementRecommended readings: portions of Asudeh (in preparation)

Friday, 28 June GLUE in other frameworksRecommended readings: Asudeh and Crouch (2002c)

2 Readings

Besides the readings listed above, we recommend the following papers for people interested in learning more aboutGLUE.

� Introductory and overview material: Dalrymple et al. (1993), Dalrymple et al. (1995), Dalrymple et al. (1999),Dalrymple (2001)

� Formal and computational issues: Dalrymple et al. (1997a), Gupta and Lamping (1998), Crouch and van Gen-abith (2000)

� Quantification: Dalrymple et al. (1997b)

� Ellipsis: Crouch (1999)

� Anaphora: Dalrymple et al. (1997b), Crouch and van Genabith (1996), Dalrymple (2001, Chapter 11)

� Resource management: Kehler et al. (1995), Asudeh (2000), Kuhn (2001), Asudeh (2002), Asudeh (in prepara-tion)

� GLUE in syntactic frameworks other than LFG: Asudeh and Crouch (2002c) (HPSG), Frank and van Genabith(2001) (Lexicalized Tree Adjoining Grammar), Asudeh and Crouch (2001) (Categorial Grammar, context-freegrammars), Hepple (1999) (D-Tree Grammars)

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� Underspecification: Crouch and van Genabith (1995), van Genabith and Crouch (1996a), Crouch and van Gen-abith (1996), van Genabith et al. (2001), Crouch and van Genabith (1999), van Genabith and Crouch (1999a)

� Coordination: Kehler et al. (1995), Dalrymple (2001, Chapter 13), Asudeh and Crouch (2002b)

� Phrase structure discontinuity: Kuhn (2001)

� Negative polarity: Fry (1997), Fry (1999a)

� Translation: van Genabith et al. (2001), Crouch et al. (2001)

� GLUE and semantic theories:

– Event semantics: Fry (1999b)

– (Underspecified) Discourse Representation Theory: van Genabith and Crouch (1996b), van Genabith andCrouch (1997b), Crouch and van Genabith (1995), van Genabith and Crouch (1999a)

– Dynamic semantics: van Genabith and Crouch (1997a), Crouch and van Genabith (1996), van Genabithand Crouch (1999b), van Genabith and Crouch (1999a) Crouch and van Genabith (1999), Dalrymple(2001, Chapter 11)

References

Asudeh, Ash. 2000. Functional identity and resource sensitivity in control. In Miriam Buttand Tracy Holloway King (editors), On-line Proceedings of the LFG2000 Conference. URLhttp://csli-publications.stanford.edu/LFG/5/lfg00.html.

Asudeh, Ash. 2002. A resource-sensitive semantics for equi and raising. In David Beaver, Stefan Kaufmann, BradyClark, and Luis Casillas (editors), The construction of meaning. Stanford, CA: CSLI Publications.

Asudeh, Ash. in preparation. Resumption as Resource Management. Ph.D. thesis, Stanford University.

Asudeh, Ash and Richard Crouch. 2001. Glue semantics: A general theory of meaning composition. Talk given atStanford Semantics Fest 2; handout available at http://www.stanford.edu/˜asudeh/.

Asudeh, Ash and Richard Crouch. 2002a. Derivational parallelism and ellipsis parallelism. In Proceedings of the 21stWest Coast Conference on Formal Linguistics. Medford, MA: Cascadilla Press. To appear.

Asudeh, Ash and Richard Crouch. 2002b. Glue semantics for coordination: Reconciling discourse cohesion and theElement Constraint through proof parallelism. Presented at the Third Semantics Fest, Stanford University; handoutavailable at http://www.stanford.edu/˜asudeh/.

Asudeh, Ash and Richard Crouch. 2002c. Glue semantics for HPSG. In Frank van Eynde, LarsHellan, and Dorothee Beermann (editors), On-line Proceedings of the HPSG ’01 Conference. URLhttp://cslipublications.stanford.edu/HPSG/2/hpsg01.html.

Crouch, Richard. 1999. Ellipsis and glue languages. In Shalom Lappin and Elabbas Benmamoun (editors), Fragments:Studies in Ellipsis and Gapping. Oxford: Oxford University Press.

Crouch, Richard, Anette Frank, and Josef van Genabith. 2001. Linear Logic based transfer and structural misalign-ment. In Proceedings of the International Workshop on Computational Semantics (IWCS-4). Tilburg.

Crouch, Richard and Josef van Genabith. 1995. F-structure: A glue for QLF and UDRT? In FraCaS Deliverable D15,pp. 217–254. FraCaS.

Crouch, Richard and Josef van Genabith. 1996. Context change and underspecification in glue language seman-tics. In Miriam Butt and Tracy Holloway King (editors), On-line Proceedings of the LFG96 Conference. URLhttp://csli-publications.stanford.edu/LFG/1/lfg1.html.

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Crouch, Richard and Josef van Genabith. 1999. Context change, underspecification and the structure of glue languagederivations. In Mary Dalrymple (editor), Semantics and Syntax in Lexical Functional Grammar: The ResourceLogic Approach. Cambridge, MA: The MIT Press.

Crouch, Richard and Josef van Genabith. 2000. Linear Logic for Linguists: ESSLLI-2000 course notes. Birmingham,UK: ESSLLI. URL www.cs.bham.ac.uk/ esslli/notes/crouch. MS in preparation with CSLI Press.

Dalrymple, Mary (editor). 1999. Semantics and Syntax in Lexical Functional Grammar: The Resource Logic Ap-proach. Cambridge, MA: The MIT Press.

Dalrymple, Mary. 2001. Lexical Functional Grammar, volume 34 of Syntax and Semantics. New York: AcademicPress.

Dalrymple, Mary, Vineet Gupta, John Lamping, and Vijay A. Saraswat. 1997a. Relating resource-based semantics tocategorial semantics. In Proceedings of the Fifth Meeting on Mathematics of Language (MOL5). Schloss Dagstuhl,Saarbrucken, Germany. Reprinted in Dalrymple (1999).

Dalrymple, Mary, John Lamping, Fernando C. N. Pereira, and Vijay A. Saraswat. 1995. Linear logic for meaningassembly. In Suresh Manandhar, Gabriel Pereira Lopes, and Werner Nutt (editors), Proceedings of ComputationalLogic for Natural Language Processing. Edinburgh.

Dalrymple, Mary, John Lamping, Fernando C. N. Pereira, and Vijay A. Saraswat. 1997b. Quantifiers, anaphora, andintensionality. Journal of Logic, Language, and Information 6(3), pp. 219–273. Reprinted in Dalrymple (1999).

Dalrymple, Mary, John Lamping, Fernando C. N. Pereira, and Vijay A. Saraswat. 1999. Overview and introduction.In Mary Dalrymple (editor), Semantics and Syntax in Lexical Functional Grammar: The Resource Logic Approach.Cambridge, MA: The MIT Press.

Dalrymple, Mary, John Lamping, and Vijay A. Saraswat. 1993. LFG semantics via constraints. In Proceedings of the6th Meeting of the EACL, Utrecht, pp. 97–105. European Chapter of the Association for Computational Linguistics.

Frank, Anette and Josef van Genabith. 2001. Glue Tag: Linear logic based semantics construc-tion for LTAG - and what it teaches us about the relation between LFG and LTAG. In MiriamButt and Tracy Holloway King (editors), On-line Proceedings of the LFG2001 Conference. URLhttp://csli-publications.stanford.edu/LFG/6/lfg1.html.

Fry, John. 1997. Negative polarity licensing at the syntax-semantics interface. In Proceedings of EACL/ACL98:Joint Meeting of the 35th Annual Meeting of the ACL and the 8th Meeting of the EACL, Madrid. Association forComputational Linguistics.

Fry, John. 1999a. Proof nets and negative polarity licensing. In Mary Dalrymple (editor), Semantics and Syntax inLexical Functional Grammar: The Resource Logic Approach, pp. 91–116. Cambridge, MA: The MIT Press.

Fry, John. 1999b. Resource-logical event semantics for LFG. URLftp://ftp-csli.stanford.edu/linguistics/Papers/lfg99fry.ps. Presented at LFG99,University of Manchester.

Gupta, Vineet and John Lamping. 1998. Efficient linear logic meaning assembly. In Proceedings of COLING/ACL98:Joint Meeting of the 36th Annual Meeting of the ACL and the 17th International Conference on ComputationalLinguistics, Montreal. Association for Computational Linguistics.

Hepple, Mark. 1999. A functional interpretation scheme for D-Tree grammars. In Proceedings of the Third Interna-tional Workshop on Computational Semantics (IWCS-3), pp. 117–130. Tilburg: KUB.

Kehler, Andrew, Mary Dalrymple, John Lamping, and Vijay A. Saraswat. 1995. The semantics of resource-sharingin Lexical-Functional Grammar. In Proceedings of the 7th Meeting of the EACL, Dublin. European Chapter of theAssociation for Computational Linguistics. Reprinted in Dalrymple (1999, pp. 191–208).

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Kuhn, Jonas. 2001. Resource sensitivity in the syntax-semantics interface and the German split NP construction. InDetmar Meurers and Tibor Kiss (editors), Constraint-Based Approaches to Germanic Syntax. Stanford, CA: CSLIPublications.

van Genabith, Josef and Richard Crouch. 1996a. Direct and underspecified interpretations of LFG f-structures. InProceedings of the 16th International Conference on Computational Linguistics (COLING96), Copenhagen, pp.262–267.

van Genabith, Josef and Richard Crouch. 1996b. F-structures, QLFs and UDRSs. In MiriamButt and Tracy Holloway King (editors), On-line Proceedings of the LFG96 Conference. URLhttp://csli-publications.stanford.edu/LFG/1/lfg1.html.

van Genabith, Josef and Richard Crouch. 1997a. How to glue a donkey to an f-structure, or porting a dynamic meaningrepresentation into LFG’s linear logic based glue-language semantics. In International Workshop for ComputationalSemantics, Tilburg, Proceedings, pp. 52–65.

van Genabith, Josef and Richard Crouch. 1997b. On interpreting f-structures as UDRSs. In Proceedings ofEACL/ACL98: Joint Meeting of the 35th Annual Meeting of the ACL and the 8th Meeting of the EACL, Madrid.Association for Computational Linguistics.

van Genabith, Josef and Richard Crouch. 1999a. Dynamic and underspecified semantics for LFG. In Mary Dalrymple(editor), Semantics and Syntax in Lexical Functional Grammar: The Resource Logic Approach. Cambridge, MA:The MIT Press.

van Genabith, Josef and Richard Crouch. 1999b. How to glue a donkey to an f-structure: Porting a dynamic mean-ing representation into LFG’s linear logic based glue-language semantics. In Harry Bunt and Reinhard Muskens(editors), Computing Meaning, volume 1, pp. 129–148. Kluwer Academic Publishers.

van Genabith, Josef, Richard Crouch, and Anette Frank. 2001. Glue, underspecification and translation. In Harry Buntand Reinhard Muskens (editors), Computing Meaning, volume 2. Kluwer Academic Publishers. In press.

Wescoat, Michael T. 1989. Practical instructions for working with the formalism of Lexical Functional Grammar. URLhttp://www-lfg.stanford.edu/lfg/lfg-introductions/pracinstrucsforlfg.ps. MS,Xerox PARC.

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1

1

A Brief Overview of Glue Semantics

and Linear Logic

NASSLLI’02

The Syntax-Semantics Interface

Ash Asudeh, Dick Crouch & Mary Dalrymple

2

Overview• Introduction:

– Aims & challenges of syntax-semantics interface

• Glue semantics:

– Linear logic for meaning assembly

• Linear logic:– An idiot’s guide

3

Mapping sentences to logical forms

• Borrow ideas from compilation of programming languages (with adaptations)

Computer Program

NL Utterance

Object CodeExecution

Logical FormInference

parsecompile

parse

interpret

4

Example Semantic Representation

• F-structure gives basic predicate-argument structure, but lacks:

– Standard logical machinery (variables, connectives, etc)

– Implicit arguments (events, causes)

– Contextual dependencies (the wire = part25)

• Mapping from f-structure to logical form is systematic,but non-trivial

The wire broke

PRED

SUBJ

TENSE

break<↑SUBJ>

PRED wireSPEC defNUM sg

past

Syntax (f-structure)

∃w. wire(w) & w=part25 & ∃t. interval(t) & t<now &

∃e. break_event(e) & occurs_during(e,t) &object_of_change(e,w) & ∃c. cause_of_change(e,c)

Semantics (logical form)

5

Programming v. Natural LanguagesWhy compilation needs adaptation

1. Grammar

2. Target

3. Context dependency

4. Ambiguity

PL: simple, deterministic context freeNL: complex, mildly context sensitive; various formalisms proposed

PL: machine codeNL: various semantic formalisms proposed, e.g. DRT, SS, HIL, PT, DL,…

PL: extremely limited (variable assignments, type declarations)NL: widespread (anaphora, ellipsis, compound nouns, …)

PL: absent (by design)

NL: ubiquitous, and massive

6

Consequences for Semantic Interpretation

• Two issues arising from differences between programming languages and natural languages– Modularity

– Compositionality

2

7

The Need for Modularity

• Different grammatical formalisms – LFG, HPSG, Categorial grammar, TAG, minimalism, …

• Different semantic formalisms– DRT, Situation semantics, Intensional logic, …

• Need for modular syntax-semantics interface– Pair different grammatical & semantic formalisms

• Possible frameworks– Montague’s use of lambda-calculus– Unification-based semantics– Glue semantics (interpretation as deduction)

8

The Challenge to CompositionalityAmbiguity & context dependence

• Strict compositionality (e.g. Montague)– Meaning is a function of (a) syntactic structure, (b)

lexical choice, and (c) nothing else– Implies that there should be no ambiguity in absence of

syntactic or lexical ambiguity

• Counter-examples? (no syntactic or lexical ambiguity)– Contextual ambiguity

• John came in. He sat down. So did Bill.

– Semantic ambiguity• Every man loves a woman.• Pets must be carried on escalator• Clothes must be worn in public

9

Semantic Ambiguity

• Syntactic & lexical ambiguity in formal languages– Practical problem for program compilation

• Picking the intended interpretation

– But not a theoretical problem• Strict compositionality generates alternate meanings

• Semantic ambiguity a theoretical problem, leading to– Ad hoc additions to syntax (e.g. Chomskyan LF)

– Ad hoc additions to semantics (e.g. underspecification)

– Ad hoc additions to interface (e.g. quantifier storage)

10

Weak Compositionality

• Weak compositionality– Meaning of the whole is a function of (a) the meaning of

its parts, and (b) the way those parts are combined

– But (a) and (b) are not completely fixed by lexical choice and syntactic structure, e.g.

• Pronouns: incomplete lexical meanings• Quantifier scope: combination not fixed by syntax

• Glue semantics– Gives formally precise account of weak compositionality

11

Some Claims

• Glue semantics is a new, general approach to the syntax-semantics interface– Alternative to e.g. unification-based semantics, Montagovian

lambda-calculus

• Glue addresses syntactic & semantic modularity

• Glue addresses semantic ambiguity/weak compositionality

• (Glue may address context dependence & update)

12

Glue Semantics Dalrymple, Lamping & Saraswat 1993 and subsequently

• Syntax-semantics mapping as linear logic inference

• Two logics in semantics:– Meaning Logic (target semantic representation)

any suitable semantic representation– Glue Logic (deductively assembles target meaning)

fragment of linear logic

• Syntactic analysis produces lexical glue premises

• Semantic interpretation uses deduction to assemble final meaning from these premises

3

13

Linear Logic (in brief)

• Influential development in theoretical computer science (Girard 87)

• Premises are resources consumed in inference (Traditional logic: premises are non-resourced)

• Linguistic processing typically resource sensitiveWords used exactly once

Traditional LinearA, A→B |- B A, A –o B |- BA, A→B |- A&B A, A –o B |/- A⊗B

A re-used A consumed

A, B |- B A, B |/- BA discarded Cannot discard A

14

Glue Interpretation (Outline)• Parsing sentence instantiates lexical entries to produce

lexical glue premises

• Example lexical premise (verb “saw” in “John saw Fred”):

see : g –o (h –o f)Meaning Term Glue Formula2-place predicate g, h, f: constituents in parse

“consume meanings of g and hto produce meaning of f”

• Glue derivation Γ |- M : f

• Consume all lexical premises Γ,

• to produce meaning, M, for entire sentence, f

15

Glue Interpretation Getting the premises

PRED

SUBJ

OBJ

see

PRED John

PRED Fred

f: g:

h:

S

NP VP

V NP

John saw Fred

Syntactic Analysis:

Lexicon:John NP john:↑Fred NP fred: ↑saw V see: ↑SUBJ –o (↑OBJ –o ↑)

Premises:john: gfred: hsee: g –o (h –o f)

16

Glue InterpretationDeduction with premises

Premisesjohn: gfred: hsee: g –o (h –o f)

Linear Logic Derivationg –o (h –o f) g

h –o f hf

Using linear modus ponens

Derivation with Meaning Termssee: g –o (h –o f) john: g

see(john) : h –o f fred : h

see(john)(fred) : f

Linear modus ponens = function application

17

Modus Ponens = Function ApplicationThe Curry-Howard Isomorphism

Curry Howard Isomorphism:Pairs LL inference rules with operations on meaning terms

g –o f g

f

Fun: Arg:

Fun(Arg):

Propositional linear logic inference constructs meaningsLL inference completely independent of meaning language

(Modularity of meaning representation)

18

Semantic AmbiguityMultiple derivations from single set of premises

PRED criminal

MODSalleged

from London

f:

Alleged criminal from London Premises

criminal: f

alleged: f –o f

from-London: f –o f

Two distinct derivations:1. from-London(alleged(criminal))

2. alleged(from-London(criminal))

4

19

Quantifier Scope Ambiguity

• Every cable is attached to a base-plate– Has 2 distinct readings– ∀x cable(x) → ∃y plate(y) & attached(x,y)– ∃y plate(y) & ∀x cable(x) → attached(x,y)

• Quantifier scope ambiguity accounted for by mechanism just shown– Multiple derivations from single set of premises– More details in a later class

20

Semantic Ambiguity & Modifiers

• Multiple derivations from single premise set– Arises through different ways of permuting

X –o X modifiers around a X skeleton

• Modifiers given formal representation in glue as X –o X logical identities– E.g. an adjective is a noun –o noun modifier

• Modifiers prevalent in natural language, and lead to combinatorial explosion– Given N f –o f modifiers, N! ways of

permuting them around f skeleton

21

Packing & Ambiguity Management• Exploit explicit skeleton-modifier of glue

derivations to implement efficient theorem provers that manage combinatorial explosion– Packing of N! analyses

• Represent all N! analyses in polynomial space• Compute representation in polynomial time• Read off any given analysis in linear time

– Packing through structure re-use• N! analyses through combinations of N sub-analyses• Compute each sub-analysis once, and re-use

• Not the topic of this course, however

22

Summary• Glue: semantic interpretation as (linear logic) deduction

– Syntactic analysis yields lexical glue premises– Standard inference combines premises to construct sentence

meaning

• Resource sensitivity of linear logic reflects resource sensitivity of semantic interpretation

• Gives modular & general syntax-semantics interface• Models semantic ambiguity / weak compositionality• Leads to efficient implementations

Idiot’s Overview of Proof Theory & Linear Logic

1. Curry Howard Isomorphism

� Proofs as first-class objects

� Mechanism by which glue derivations assemble meaning terms

2. Linear Logic

� Motivated by proof theoretic considerations

1

What You Need to Remember

Linear Logic Curry Howard

Traditional:

� � � � � � �

� � � � � � � � �

Re-use �

� � � � �

Discard �

Linear:

� � ��

� � ��

Cannot re-use �

� � � � �

Cannot discard �

� � ��

� � � � � � � �

� � � � � � �

��

� � � ��

�� ! � � � � ��

2

Proofs as First-Class Objects

Proofs as the senses of formulas:— instead of “When is A true?”, ask “What is a proof of A”?

Problem: we have no direct access to proofs— only to their syntactic representations as derivations in some proof system

— syntax of derivations can introduce spurious distinctions

Aim: find the correct identity criteria for proofs— “No entity without identity”

Esoteric, logician’s concern? No.

3

Parsing as Deduction

Context Free Grammar Deductive GrammarS " NP VPVP " V NPPP " P NPNP " NP PPVP " VP PPNP " Det N

NP# # VP $ � � S $

V# # VP $ � � VP $

P# # NP $ � � PP $

NP# # PP $ � � NP $

VP# # PP $ � � VP $

Det# # N $ � � NP $

S

NP VP PP

John V NP P NP

saw a man with a telescope

Corresponds to two distinct proofs of:

% NP & , & V ' , ' Det ( , ( N ) , ) P * , * Det + , + N , � % S ,

John saw a man with a telescope

Distinct proofs/parses have distinct meanings

4

Semantics of Proofs:Implication Elimination as Functional Application

Natural deduction rule for (intuitionistic) implication elimination:

� � � ��

�

� � � : function � that takes a proof � of � to give a proof �� of �

��

� � � ��

(Also works for linear implication,� � )

5

Implication Introduction as Lambda Abstraction

Natural deduction rule for implication introduction

� � � ��

� � � �

� � �

Assuming � allows one to prove � .

Therefore, discharging the assumption, � � � , one proves � � �

With proof terms

� � � � ��

� � � ��

6

Identity Criteria for Proofs

Two ‘proofs’ of � � � � � � :

� � � ��

�

� � � & � � ��

��

� � � ��

�

These are not really distinct proofs:

7

Lambda-Equivalence of Proof Terms

Include proof terms in previous derivations:

��

��

� � � � & ��

��

� � ��

� � � ��

Note: � � � �� ! ��

! -equivalence of proof terms: semantic identity of derivations.

8

Curry-Howard Isomorphism (CHI)

CHI = Pairing of proof rules with ! -operations on proof termsBut doesn’t work for all logics, or proof systems

Intimate relation between logic and type-theory.Normalization of proofs isomorphic to � -reduction of proof terms

Defines interesting identity criteria for proofsSyntactically distinct derivations corresponding to same proof

9

Limitations of Curry Howard

Curry-Howard gives non-trivial identity criteria for proofs, but:

� It only works for certain logicse.g. intuitionistic logic, but not classical logic

� It only works for natural deduction proofs

� It handles ‘parasitic’ rules inelegantly

� � �

� � ��

��

� � � #�

� is a parasitic formula:has nothing to do with the formula, � � � , being eliminated

‘The shame of natural deduction’ (Girard)

10

Linear Logic and Proof Identity

Girard’s motivation for linear logic:More general identity criteria for proofs

Method:Step back from natural deduction to sequent calculus

— To get rid of parasitic rules

Remove structural rules to get linear logicShow how this enforces interesting identity criteriaOther logics can be coded in linear logic

Can’t cover all of this here.

11

Sequent Calculus

Alternative proof system: sequential version of natural deduction

� � � ��

� � � � � �

� � � � � ��

� � � � �

� � � � � � ��

� � � � � �

� � � ��

� � � � �

Rule � � discharges ‘assumption’ �

12

Poor Identity Criteria from Sequent Calculus

Both the sequent derivations� � � � � �

� �

� � � � � � ��

� � � � � � � � � ��

� � � � � � � � � � � � �

� � � � � ��

� � � � � � ��

� � � � � � � � � ��

� � � � � � � � � � � � �

correspond to the same natural deduction proof

� � � ��

�

� � � ��

��

� � �

Different sequentializations of one ND proof— cf leftmost/rightmost context-free derivations of one parse tree

13

Structural Rules

� � � : a subset of � follows from a subset of �

Weakening: taking subsets(allows fake dependencies)

� � �

Weakening �

� � � �

� � �

Weakening �

� � � �

Contraction: repeating set elements(allows duplication & multiple discharge of assumptions)

� � � � �

Contraction �

� � � �

� � � � �

Contraction �

� � � �

14

Consequences of Removing Structural Rules

Structural rules implicit in traditional logic.

If we remove them

� Derivations are from multisets of premises,not sets of premises

� We preclude fake dependencies and multiple discharge of assumptions.

� We tighten identity criteria for proofs.

� We get two distinct versions of each familiar connective.

� And we get linear logic.

15

Contraction & Weakening: Premises as Resources

� � � � � ��

In traditional logic:— � follows from some subset of �� & ��

— sets allow permutation and duplication of premises (contraction)

— subsets allow discarding premises (weakening)

In linear logic— � follows from the multiset �� & ��

— multisets allow permutation of premises only

No duplication or discarding: premises become resources.

Permutation: order of premises remains immaterial

16

Alternate Rule for Conjunction ( � � � )

Usual Alternate(Additive) (Multiplicative)

� � � � � ��

� � � � �

� � � � � ��

� � � � � �

Where � � is a special case of � � � : � � � .

Rules � � and � � � interderivable given contraction and weakening

Similarly for alternative � � rules:

� � � � ��

� � � � � � �

� � � � � � ��

� � � � � � �17

Interderivability given Contraction & Weakening

� � � from � � �

� � � � � ��

� � � � � �

Contraction �

� � � � �

� � � � from � �

� � �

Weakening �

� � � �

� � �

Weakening �

� � � ��

� � � � � �

18

Multiplicative and Additive Conjunction

Without contraction & weakening, rules define alternate connectives

Multiplicative conjunction (tensor)

� � � � � � �

� � � � � �

� � � � � �

� � � � � �

� and � bundled to prove� �� Premises� and� bundled together

Additive conjunction (with)

� � � � � �

& �

� � � � �

� � � �

& �

� � � � � �

� proves� and proves� � plus something that can prove�

But not both at once (and can prove� ) proves

19

A Plethora of Connectives

� � � Consume � to produce�

� � � Both � and� simultaneously available

� � � Either � or� available: your choice which

� � Either � or� available: random selection

� � Can duplicate or discard �

Menu: $5 � � � � � ��

Fish ��

Chips � � � ��

Soup or Salad ��

Fruit or cheese � � � � �� ! ! � ! �

(depending on availability) �

Coffee � " " ! !

(free refills) �# � " " ! ! $

20

(Prawitz) Natural Deduction for (Multiplicative) Linear Logic

� � � � ��

��

� � � � � � � � � � � � � �

� � � � �� #�� #let be � � in � � �

� ! ��

� � � � � � � � � must be linear — exactly one occurrence of bound

� � � ��

Pairing � � � without projections onto � and �

Eliminated instead by: let � � � be � � � in � � " � � � � � � � �21

Linear and Non-Linear Assumptions

� Premises are just undischarged assumptions

� Needn’t discharge assumptions in order they are introduced

� Non-Linear only:Can discharge multiple (co-indexed) assumptions at once

� � ��

�� $� � ��

�� $� � �� &��

� Non-Linear only:Can discharge non-existent assumptions

�� $� � � � '� � � � � � &� � ��

22

The Syntax-Semantics Interface: Theory and ImplementationTuesday, 25 June 2002

Introduction to LFG, GLUE;some simple sentences; modification

1

Syntax and semantics: In the beginning

Montague (1974) on adjectives modifying nouns

If � is an adjective meaning and � is a noun meaning, then the meaningof [adjective noun] is � applied to � , � � � � .

� � Adj and � � N � � � � � � N

Example: the meaning of “Swedish man” isthe meaning of “Swedish” applied to the meaning of “man”.

The meaning of a phrase is obtained by combining the meanings of theparts of the phrase as specified by the rule.

2

Constructional parochiality

. . . the meaning of [adjective noun] is � � � � .

Meaning assembly instructions are specifiedfor each phrase structure configuration.

3

Semantic composition imposes requirementson syntactic structure

. . . the meaning of [adjective noun] is � � � � .

Syntactic unit needed for each meaning combination step:

[Adj [Adj [Adj N] � ] � ] �

4

But phrase structure varies from language to language:it’s not a good guide for semantic composition.

English: ‘The small children are chasing the dog.’

IP

NP

Det

the

N’

AdjP

small

N

children

I�I

are

VP

V

chasing

NP

Det

the

N’

N

dog

5

Warlpiri:

kurdu-jarra-rlu

child-dual-erg

kapala

pres

maliki

dog.abs

wajilipi-nyi

chase-nonpast

wita-jarra-rlu

small-dual-erg

‘The two small children are chasing the dog.’

IP

NP

N

kurdu-jarra-rlu

child-dual-erg

I�

I

kapala

pres

S

NP

N

maliki

dog-abs

V

wajilipi-nyi

chase-nonpast

NP

N

wita-jarra-rlu

small-dual-erg

6

F-structure for English and Warlpiri‘The small children are chasing the dog’:

��

��

��

��

��

��

��

��

�

PRED ‘chase’

SUBJ

��

��

��

PRED ‘children’

SPEC ‘the’

MODS

� �

PRED ‘small’

� ��

OBJ ��

PRED ‘dog’

SPEC ‘the’

�

�

7

Semantic composition in LFG:F-structures, semantic projections, and meanings

NP

David

� ��

PRED ‘David’

�

�

�

8

Meaning assembly and linear logic:

Composing meanings via deduction

� Logic of meanings (semantic level):the level of meanings of utterances and phrases

� Logic for composing meanings (‘glue’ level):the level responsible for assembling the meanings of parts to get themeaning of the whole

9

David yawned.

� :

��

��

PRED ‘YAWN � SUBJ � ’

SUBJ � :

�

PRED ‘DAVID’

��

David David � �

yawn �� yawn ��

Meanings of words and how they combine with other meanings arespecified logically;

meaning composition then proceeds according to rules of logic.

yawn � David � � �

10

Expressive flexibility: Different meaning languages

David yawned.

� :

��

��


SUBJ � :

�

PRED ‘DAVID’

��


Lambda DRT:

� � � David � yawn � � ��

xx = Davidyawn(x)

� �

Different meaning languages compatible with glue approach.

11

Expressive flexibility:Different semantic theories with same syntax

David tried to leave.

� :

��

��

��

��

��

��

PRED ‘TRY � SUBJ,XCOMP � ’

SUBJ

�

PRED ‘DAVID’

�

XCOMP ��

�

PRED ‘LEAVE � SUBJ � ’

SUBJ

�

�

Propositional theory of control:try � David � leave � David � � � �

Property theory of control:try � David � �� leave ��

12

Lexical entries:

David N ( � PRED) = ‘DAVID’

David � � yawned V ( � PRED) = ‘YAWN � SUBJ � ’

�� yawn �� SUBJ � � �

13

Phrase structure rules:

IP � � NP( � SUBJ) = �

I�� = �

I� � � I

� = �

VP

� = �

VP � � V

� = �

NP � � N

� = �

14

Annotated phrase structure tree:

IP

NP

( � SUBJ) = �

N

� = �

David

( � PRED) = ‘DAVID’

David � �

I�� = �

VP

� = �

V

� = �

yawned

( � PRED) = ‘YAWN � SUBJ � ’

�� yawn �� SUBJ � � �

15

Instantiated annotations:

� � is the f-structure corresponding to the node labeled IP

IP

NP

( � � SUBJ) = �

N

� =

David

( PRED) = ‘DAVID’

David �

I�� = � �

VP

� � = � �

V

� � = �

yawned

( � PRED) = ‘YAWN � SUBJ � ’�� yawn �� SUBJ � � �

16

IP

NP

N

David

I�

VP

V

yawned

( � � SUBJ) = �

� =

( PRED) = ‘DAVID’David �

� � = � �

� � = � �

� � = �


�� yawn ��

17

IP

NP

( � � SUBJ) = �

N

� =

David

( PRED) = ‘DAVID’

I�� = � �

VP

� � = � �

V

� � = �

yawned


� � � � � � � � � � :

��

��


SUBJ � � :

�

PRED ‘DAVID’

��

David David �


18

David yawned.

� ��

��

PRED ‘yawn’

SUBJ ��

PRED ‘David’

��

�

David David �


19

Choice of glue language: linear logic, a resource logic

Translation rules in Montague semantics have the property that the translationof each component of a complex expression occurs exactly once in the trans-lation of the whole. . . . That is to say, we do not want the set S [of semanticrepresentations of a phrase] to contain all meaningful expressions of IL whichcan be built up from the elements of S, but only those which use each elementexactly once. (Klein and Sag, 1985, page 172)

linear implication:�

CORRECT: � � � � � � � � �

INCORRECT: � � � � � � � � � � �

INCORRECT: � � � � � � � � � � � � �

20

Meaning constructor premises for David yawned

David David �


Curry-Howard Isomorphism

� � �

� � � � �

� ��

21

David � The subject semantic structure is associated withthe meaning David .

�� yawn ��

If a semantic resource for the subject is found, aresource � can be produced. On the meaning side,the predicate yawn is applied to the subject meaning

� to produce the meaning yawn �� for the sentence.


We have produced a semantic structure � for the sen-tence, associated with the meaning yawn(David).

22

Natural deduction-style proof for David yawned

�� yawn �� David �


yawn David


23

David selected Chris.

� ��

��

��

��

PRED ‘select’

SUBJ � ��

PRED ‘David’

�

OBJ � ��

PRED ‘Chris’

�

�

� �

�

David David � �

Chris Chris � �

select �� select ��

24

Chris � � The object semantic structure � is associated with themeaning Chris .

David � � The subject semantic structure � is associated withthe meaning David .

�� select ��

If semantic resources for the object � and subject �

are found, a resource � can be produced. On themeaning side, the two-place predicate select is ap-plied to the object meaning� and then the subjectmeaning� to produce the meaning select �� forthe sentence.

select � David � Chris � � �

We have produced a semantic structure �

for the sentence, associated with the meaningselect(David,Chris).

25

Natural deduction-style proof for David selected Chris

Chris � � �� select ��

�� select �� Chris � � � � � David � �


Chris select

�� select �� Chris � � � � � David


26

The glue approach

� Exploits the ability of the logic to name things, to capture the f-structuralsyntactic constraints on semantic composition

� Enables a flexible interface between syntax and semantics: no unrea-sonable syntactic requirements imposed by theory of semantic compo-sition; no unreasonable semantic requirements imposed by syntactictheory

� Exploits the resource-conscious properties of linear logic to allow mod-ification and to ensure that each word contributes exactly once to themeaning

27

We have seen:

� Architecture of LFG: lexical entries, phrase structure rules, semanticpremises

� Deduction at the syntax-semantics interface � Sentence meanings

Next:

� Nouns: syntax and semantics

� Adjectives as noun modifiers

28

Swedish man

��

�

PRED ‘man’

ADJ

� �

PRED ‘Swedish’

� ��

��

VAR v:[ ]

RESTR r:[ ]

�

man �� man ��

Swedish � � � �� Swedish ��

General form of modifiers: � � � � �No need for syntactic units mirroring

meaning composition steps.

29

Nouns: Syntax and semantics

man

��

PRED ‘man’

�

� ��

VAR � [ ]

RESTR � [ ]

�

�� man ��

30

Noun modification by intersective adjective

Swedish man

��

�

PRED ‘man’

ADJ

� �

PRED ‘Swedish’

� ��

��

VAR � [ ]

RESTR � [ ]

�

�� Swedish �� man ��

Intersective modification:

� is in the intersection of men and Swedish things.

31

Noun modification by gradable adjective(Montague, 1974; Kamp, 1975; Kennedy, 1997)

big mouse

��

�

PRED ‘mouse’

ADJ

� �

PRED ‘big’

� ��

��

VAR � [ ]

RESTR � [ ]

�

�� big �� mouse ��

� is a mouse, and is big relative to individuals that have the property� ;here� is the property of being a mouse.

32

�� big �� mouse ��

What is� ? – A contextually-salient property of�

(McConnell-Ginet, 1979; Pollard and Sag, 1994; Kennedy, 1997)

The Linguistics Department has an important volleyball game coming upagainst the Philosophy Department. I see the Phils have recruited Juliusto play with them, which means we are in real trouble unless we can finda good linguist to add to our team in time for the game. (Pollard and Sag,1994)

33

Noun modification by intensional adjective(Kamp, 1975; Siegel, 1976)

former senator

��

�

PRED ‘senator’

ADJ

� �

PRED ‘former’

� ��

��

VAR � [ ]

RESTR � [ ]

�

�� former � senator ��

� is an individual that stands in the former relation to the property ofbeing a senator.

34

We have seen:

� Noun modifiers: Syntax and semantics

Next:

� How modified noun meanings are obtained by semantic deduction

35

Swedish man

��

�

PRED ‘man’

ADJ

� �

PRED ‘Swedish’

� ��

��

VAR � [ ]

RESTR � [ ]

�


Swedish � � � �� Swedish ��

General form of modifiers: � � � � �

36

�� man ��

The meaning �� man �� is associated withthe implicational contribution �� .

� � � �� Swedish ��

Glue: The meaning constructor consumesthe noun contribution � � � and produces anew modified meaning which is also associ-ated with �� . Meaning: apply the function

� � � Swedish �� to the unmodifiedmeaning contributed by man, �� man �� .

�� Swedish �� man ��

We have produced a modified meaning

�� Swedish �� man �� associated withthe implicational contribution �� .

37

big mouse

��

�

PRED ‘mouse’

ADJ

� �

PRED ‘big’

� ��

��

VAR � [ ]

RESTR � [ ]

�

mouse �� mouse ��

big �� big ��

big � mouse � �� big �� mouse ��

38

former senator

��

�

PRED ‘senator’

ADJ

� �

PRED ‘former’

� ��

��

VAR � [ ]

RESTR � [ ]

�

senator �� senator ��

former � � � �� former � � ��

former � senator � �� former � senator ��

39

Scope ambiguity =Different deductions from the same premises

alleged criminal from London

��

��

��

��

��

��

PRED ‘criminal’

ADJ��

� ��

�

PRED ‘alleged’

�

��

�

PRED ‘from’

OBJ

�

PRED ‘London’

��

� ��

��

��

VAR � [ ]

RESTR � [ ]

�

criminal �� criminal ��

alleged � � � �� alleged � � ��

from-London � � � �� from �� London � � � ��

40

Two deductions from the same premises:

alleged � criminal � from-London �

�� alleged � �� criminal �� from �� London � ��

alleged � criminal � from-London �

�� alleged � criminal �� from �� London � � ��

41

We have seen:

� Nouns and their modifiers at the syntax-semantics interface: How mod-ified meanings are obtained

Next:

� A puzzle: Modifying a modifier

42

‘Recursive modification’ (Kasper, 1995)

Swedish

� � � �� Swedish ��

apparently Swedish

� � � �� apparently � Swedish ��

General problem for categorial-style analyses.

43

Solution: Decomposition of meaning of modifiers.

��

ADJ

��

�

PRED ‘Swedish’

� ��

� ��

VAR � [ ]

RESTR � [ ]

�

� �

VAR � � [ ]

�

Swedish1 �� Swedish ��

Swedish2 � � � � � � ��

44

Original adjective meaning Swedishdeducible from Swedish1 and Swedish2


Swedish2 � � � � � � ��

Swedish1 � Swedish2 �

� � � �� Swedish ��

45

[[apparently Swedish] man]

� ��

VAR � [ ]

RESTR � [ ]

�

��

��

��

��

PRED ‘man’

ADJ

��

��

�

PRED ‘Swedish’

ADJ

��

�

PRED ‘APPARENTLY’

� ��

� ��

��

� �

VAR � � [ ]

�

� �

VAR � � [ ]

�

�� apparently � Swedish �� man ��

46

Combining apparently with Swedish1

apparently � � � �� apparently ��


apparently � Swedish1 �

�� apparently � Swedish ��

47

Combining app-Sw, Swedish2, and man

app-Sw �� apparently � Swedish ��

Swedish2 � � � � � � ��

� ��


app-Sw � Swedish2 � man �

�� apparently � Swedish �� man ��

48

Dalrymple, M. (2001). Lexical Functional Grammar , volume 34 of Syntax and Seman-tics. Academic Press, New York.

Dalrymple, M., Lamping, J., Pereira, F. C. N., and Saraswat, V. A. (1999). Overview andintroduction. In Semantics and Syntax in Lexical Functional Grammar: The ResourceLogic Approach (M. Dalrymple, ed.). The MIT Press, Cambridge, MA.

Kamp, H. (1975). Two theories about adjectives. In Formal Semantics of Natural Lan-guage (E. L. Keenan, ed.), 123–155. Cambridge University Press, Cambridge, UK.

Kasper, R. (1995). Semantics of recursive modification.Handout for HPSG Workshop Tubingen, June 1995. URL:ftp://ling.ohio-state.edu/pub/HPSG/Workshop.Tue.95/Kasper/

Kennedy, C. (1997). Projecting the Adjective: The Syntax and Semantics of Gradabilityand Comparison. Doctoral dissertation, University of California, Santa Cruz.

Klein, E. and Sag, I. A. (1985). Type-driven translation. Linguistics and Philosophy 8,163–201.

McConnell-Ginet, S. (1979). On the deep (and surface) adjective ‘good’. In GrammaticalStudies: Semantics and Syntax (L. R. Waugh and F. van Coetsem, eds.). E.J. Brill,Leiden.

Montague, R. (1974). English as a formal language. In Formal Philosophy (R. Thoma-son, ed.). Yale University Press, New Haven.

49

Pollard, C. and Sag, I. A. (1994). Head-Driven Phrase Structure Grammar . The Univer-sity of Chicago Press, Chicago.

Siegel, M. E. A. (1976). Capturing the Adjective. Doctoral dissertation, University ofMassachusetts at Amherst.

Quantification

NASSLLI’02The Syntax-Semantics Interface

Weds 26th June

1

The Problem with Quantifiers

Meanings for proper names are straight forwardEntity denoting arguments to which predicates apply

��

��

But quantified NPs don’t act as simple argumentsSomeone yawned � ��

Treat quantified NPs as functions looking for predicates as argument

��

��

2

Digression: Type Raising

Can also treat proper names as functions looking for predicates, via type raising

��

� � �� !"��

��

Type raising is often regarded as deeply mysterious.

In glue, it is just a consequence of the standard inference rules for implication

3

Scope Ambiguity: Everyone saw someone

Suppose we have the instantiated premises

# ��

# �� $ � � � � � � � � � ��

# � % � � � � � � � � � � � % � � � � � � � � � �

There are two distinct derivations of �

& � � '( � � )* + &, "

( � � ) +( ,.-

) � � !"& � � ) ' & � � )* � � )

) � � !-( � � ) ' ( � � )* � � )

)

& � � ' ( � � )* + &, "

( � � ) +( ,.-

) � � !-( � � ) '( � � )* � � )

) � � !"& � � ) ' & � � )* � � )

)

4

One Derivation, with Meaning Terms

�� '� � �* � & � � ' ( � � )* +� � &, "

� �� ' � � �* � ( � � ) + � ( ,.-

�� ' � � * � ) � � !"

� � � �� ' � � * � & � � )

��

��

� � �� ! ��" � �� ! ��

��" � �� 5

Scope Across ClausesEvery man believed a woman yawned

Quantified NP “a woman” can scope over main or subordinate clause.

�$ � � � ��

�� # �$ � �$ � ��

�$ � � � ��

�� # �$ � �$ � ��

��

� � � �$ � � � �� # �$ � �$ � ��

To allow quantifiers to ‘float up’, glue formula universally quantifies over scoperesource, e.g.

�� $ � � � �� %& � � � � � & � � � &

where& can be any (well, almost any!) atomic semantic resource serving as thenuclear scope of the quantifier

6

F-structure & Premises

� �' (((((((((

)

PRED believe

SUBJ � �*

PRED manSPEC every +

COMP �,' ()

PRED yawn

OBJ - �*

PRED womanSPEC a +

. /0

. /////////0

# # �$ � �$ � � � � � � � � � �

# �� - � �

# �$ � � � � %& � � �$ � � � � � � � � � 1 � � � � � � � � � � � & � � � � & �

# � � � � $ � � � � � � � � � 1 � � � �

# �� %& 2 � �$ � � � - � � � � � 1 � � - � � � � � - � � & 2 � � � & 2

# � � � � � � $ � � � - � � � � � 1 � � - �

7

Building Quantified NP Meanings

# �$ � � � � �$ � � � � � � � � � 1 � � � � � � � � � � � & � � � � & �

# � � � � $ � � � � � � � � � 1 � � � �

every � '34 5 ' &* � � 5 � �6 5 ' &* * � � ' & � � 7 " * � � 7 " man � 34 5 ' &* � � 5 � �6 5 ' &*

every(man) � ' & � � 7 " * � � 7 "

# $ � � � � �� 1 � � � � : resources form semantic projection of �

# � � 1 � � � � : very loosely, resource corresonding to Nbar of the NP �

8

Derivations

� 3 � 5 � ' �4 � � � � � �� 3 � '� � �� '� � �4 � � � �� 4 � � ' �* * * *

� � � (� 7- � ' � � � 7- * � � 7-

' � � � ( * � � (

(

+ &, & � � ' ( � � )*

( � � )

)& � � )

� 7 " � ' & � � 7 " * � � 7 "

' & � � )* � � )

)

�� '� � �4 � � � �� 3 � 5 � ' �4 � � �� 3 � '� � �4 � � ' �* * * *

� � � ( + �,(

+ &, & � � ' ( � � )*

( � � )

)& � � )

� 7 " � ' & � � 7 " * � � 7 "

' & � � )* � � )

)� � � )

� 7- � ' � � � 7- * � � 7-

' � � � )* � � )

)

9

A Non-Derivation

If the “a woman” quantifier can float up, why can’t “every man” float down, to givethe ill-formed meaning

# �$ � �$ � �� $ � � � ��

The quantifier meaning constructor �$ � � �� %& � � � � � & � � � &

says: freely choose an (atomic) scope& , provided that& depends on � .

Dependency is transitive:

# “woman(k) sub-clause(h) main-clause(f)”Implies “woman(k) main-clause(f)”Hence subordinate quantifier (k) can scope over main clause (f)

# “sub-clause(h) main-clause(f)” and “man(g) main-clause(f)”Does not imply “man(g) sub-clause(h)”Hence main quantifier (g) cannot scope over subordinate clause (h)

10

� and1 Resources

To get scoping right, we need to restrict possible scopes to semantic resourcesthat correspond to propositional meanings.

We thus sort all semantic resources into two types:

# 1 -resources (truth value denoting)

# � -resources (entity denoting)

The quantified variable,& in �$ � � � � � � � %& � � � � � & � � � &

needs to be restricted to range over only atomic1 -resources.

Note that � is an � -resource.

From the glue formula � � � � � & 6 � � � & 6

we can read of the type of the meaning expression: � � � � 1 �� 1 � .Experiment: see what happens of you allow the variable& to range over type �

resources.11

Complex NPsEvery representative of a company saw a sample

Standard example to test correctness of theory of scope

Simple permutation of 3 quantifiers would suggest 3! = 6 scopings

But there are only 5: cannot have rep sample company

Missing scope has free variables and vacuous quantification

% � � � � � � � � ��

� � � � � $ � � �

� � � � � � � � � � � � � �� Free variables � undischarged linear logic assumptionsVacuous quantification � discharge of non-existent assumptionsGlue prohibits both!

12

Every representative of a company saw a sample

every-rep : � �� ' 5 � � � � � * � � � �

of : � � � � � ��

a-company : ' � � � � � * � � �

saw : 5 � � � � � � � )�

a-sample : ' � � � � � � * � � � �

Narrow scope � � Wide scope � � Impossible scope

� � � � � ��' � � � � � * � � �

� �� ' 5 � � � � � * � � � �

' 5 � � � � � * � � � �

� � � � ' 5 � � � )� *

� � � � )�' � � � � � � * � � � �

)�

� � � � � ��+ � �,� ��

� �� ' 5 � � � � � * � � � �

' 5 � � � � � * � � � �

� � � � ' 5 � � � )� *

� � � � )�' � � � � � � * � � � �

)�� )�' � � � � � * � � �

)�1. � � � � � ��

2. + � �,

3. � ��

4. � �� ' 5 � � � � � * � � � �

5. ' 5 � � � � � * � � � �

6. 5 � � � ' � � � � )� * scope � �

7. ' � � � � � * � � � � ��

X. 5 � � � ' � � � � )� * INVALID

9. ' � � � � � � * � � � � scope � �

10. 5 � � � )�11. )� scope� � : 5, 10X. (2) undischarged

13

Cooper Storage

Mechanism to generate quantifier scopings

# Meanings a pair of: Main meaning, Quantifier store

# Operation 1: Store a quantifier

# Give quantified NP a variable meaning,� , in main meaning

# Place quantifier % �� in store

# Operation 2: Retrieve a quantifier

# Remove % �� from storage

# Bind variable� in main meaning by %

# Final meaning must have empty quantifier store

# Complex constraints on retrieval (nested Cooper storage) to avoid free vari-ables & vacuous quantification

Glue account of scope is rational reconstruction of (nested) Cooper storage

14

Cooper Storage v. GlueEveryone saw something

Cooper Storage Glue

Meaning Store

� � � � �� ' � � * []

� � �� '� � * + � � �� , store x

�� '� � �* + � � �� , store y

� � � �� '� � �* + � � � �, retrieve x

�� '� � �* +, retrieve y

��

� � � !"� � � � � ��

� � � !- � � � � � � � ��

�

# Storage = Assumption introduction

# Retrieval = Assumption discharge

# Proper assumption discharge accounts for nested storage

Glue requires no scoping mechanism beyond standard deduction rules

15

Expressing Scope Constraints

Can express scope constraints as constraints on structure of glue derivations(Crouch & van Genabith)

NP outscopes NP � :# Last occurence of in (normal form) derivation must occur below last occur-

rence of �e.g.

& � � ' ( � � )* + &, "

( � � ) +( ,.-

) � � !"& � � ) ' & � � )* � � )

) � � !-( � � ) ' ( � � )* � � )

)

16

Quantifiers as Modifiers

# Defining modifiers

# Skeletons and modifiers

# Quantifiers as dependent modifiers: skeleton + modifier

17

Problems with Defining Glue Modifiers

Previous class:

# Modifiers as � � � � identities

# Ambiguity through different ways of permuting � � � � around � skeleton(Leads to efficient proof search algorithms)

But over-simplistic to define a glue modifier as a logical identity of the form � � � �

For example

� �� # � � � �� # �� # � � � # ��

Want to treat both formulas as modifiers

Also, want to generalize definition of modifier so that quantifiers

� � � � � � � � �

can be seen as (dependent) modifiers

18

Polarity in Glue Formulas

Can classify all linear logic subformulae by polarity:

# Positive: production of resources

# Negative: consumption of resources

Polarity rules for implication

# ��

��

Atomic polarities for some positive formulas

# � � � � � � # � � � � � �

� � � � � � �

�� # � � � � � �� #� �

� � � � � � �� # � � � � � #� �

� � � � � � � � � � � � � �

19

Skeleton & Modifier Occurrences

Divide the atomic subformulas in a (positive) formula into modifier and skeletonoccurrences

# A positive/negative atomic subformula is a modifier occurrence iff# The formula contains a corresponding negative/positive atomic subfor-

mula, and

# The connective linking the two subformulas containing these occurrencesis a positive implication

# An atomic subformula is a skeleton occurrence iff it is not a modifier occur-rence

20

Formulas with modifier occurrences underlined

# � � � � � � # � � � � � �

# � � � � � � �

# �� # � � � � � �� #� �

# � � � � � � �� # � � � � � #� �

# � � � � � � � � � � � � � �

# � � � � � � � � � � � � � � �

21

Pure and Impure Modifiers

# Pure modifier:Formula contains only modifier occurrences

e.g. �� # � � � �� # �

# Impure modifier:Formula contains some skeleton and some modifier occurrences

e.g. � � � �� ,� � � � � � � � � , � � � � � � � � �

# Purifiable modifier:An impure modifier that can be rearranged so that there is just one sub-formula containing

all the modifier occurrences and no skeleton occurrences

e.g. � � � �� ,� � � � � � � � �

Purifiable modifiers can be rearranged to give expressions of the form

� � �� " � � '� � � � � ' � � �� 5 � � � �* * � � � *

Note that quantifiers such as � � � � � � � � � are not purifiable.

22

Non-Purifiable = Dependent

A quantifier, like � � � � � � � � � , is a dependent modifier.

It modifies an � that is missing / dependent on a � , to give an � where thedependency has been discharged.

(The � has as a free variable meaning� that gets bound when the dependencyis discharged)

23

Insertion of Dependent Modifier

� ��

��

�

...

+ � � � � � � � � �

�

� ��

��

��

�

...

24

Parallelism in Ellipsis

NASSLLI 2002, Stanford

The Syntax-Semantics Interface

Ash Asudeh, Dick Crouch, Mary Dalrymple

June 26, 2002

1 Introduction

� A central topic in work on ellipsis:Parallelism between missing VPs and their antecedents

� Evidence that parallelism is conditioned bothsyntactically and semantically

� Result: complex hybrid principles that regulate both syntactic structures andtheir interpretations (e.g., Fox 1995, 2000)

� An alternative, unified account based on parallelism of semantic derivations (i.e.,proofs) in GLUE

� Captures the insights of hybrid accounts, but

� Conceptually simpler

� Empirically superior

� Theoretically important:

� An implicit argument for a level of semantic representation

� Favours indirect translation (Montague 1973)over direct model-theoretic interpretation (Montague 1970)

� Key claims:

1. Semantic derivations are a useful and interesting level of linguistic representa-tion.

2. Semantic derivations are the proper locus for calculating ellipsis parallelism.

The Syntax-Semantics Interface NASSLLI 2002 June 26, 2002 2

2 The Data

� Our focus: scope parallelism in ellipsis(among many others: Sag 1976, Williams 1977, Hirschbuhler 1982)

� Terminology

(1) Gonzo laughed. Andrew did, too.

Ellipsis source Ellipsis target

� The Wide Scope Puzzle:A scopally ambiguous sentence is disambiguated to surface scope when it is thesource for VP-ellipsis (Sag 1976).

(2) A rhino sat in every corner. Babar did, too.

� Canadian Flags:If the subject of the target is also quantificational, both inverse and surface scopeare possible for the source and target sentences (Hirschbuhler 1982).

(3) An American flag hung in front of every window. A Canadian flag did, too.

(4) A rhino sat in every corner. An elephant did, too.

� The scope of source and target must be parallel:both surface or both inverse

� These issues have been resurrected in important recent work by Fox (1995, 2000)

� This work has faced conceptual, theoretical, and empirical challenges(Asher et al. 1997, 2001, Jacobson 1998, Johnson and Lappin 1997, 1999)


2.1 Fox’s Theory

� Based on the assumptions in (5) and (6), Fox (2000) derives generalization (7).

(5) Scope economy: [Scope-shifting operations] that are not forced for typeconsiderations must have a semantic effect.(Fox 2000:23)

(6) Parallelism: In an ellipsis/phonological reduction construction the scopalrelationship among the elements in

�� must be identical to the scopal rela-tionship among the parallel elements in

�� .(Fox 2000:33)

(7) The Ellipsis Scope Generalization (ESG): A sentence

will disambiguateits syntactic image

(in favor of surface scope), whenever

is semanti-cally equivalent under surface and inverse scope (i.e, whenever

is sco-pally uninformative).(Fox 2000:34)

� The ESG makes predictions that are in line with Sag’s and Hirschbuhler’s observa-tions.

1. Proper names are not scopally ambiguous:

� Target in (2) is semantically equivalent under surface and inverse scope

� Source is correctly predicted to have only surface scope

2. In (4) the target is not semantically equivalent under surface and inverse scope

� The source is predicted to allow inverse scope

� Unlike the version of the ESG in Fox (1995), this version is symmetric: the targetcan force surface scope in the source or vice versa.


2.2 Counterexamples

(8) At least one MP attended every committee meeting, and Bill did too.(Lappin 1993:265)

(9) An intern must see each patient before Dr. Krankheit will.(Shieber et al. 1996:10, (14))

� Fox (1995): the stage-/individual-level distinction between predicates (Kratzer 1989,1995) is crucial; the ESG only holds for individual-level predicates.

� There are counterexamples even with individual-level predicates(Asher et al. 1997, 2001, Jacobson 1998, Johnson and Lappin 1997, 1999)

(10) At least one natural number other than one divides into every prime num-ber, and one does too.

(11) At least two cabinet members bear responsibility for each government de-partment, and Tony Blair does too.(Johnson and Lappin 1999:34, (38a–b))

� Fox (2000:35, fn. 20):“many ill-understood factors enter into the analysis of [(10) and (11)]”

� “[(10)] is a ‘lawlike’ sentence about arithmetic”� “[(11)] very likely involves incorporation of an indefinite quantifier (some re-

sponsibility)”

� Regarding the comment on (10):

� The ESG is a generalization about linguistic representation.

� Even if sentences containing lawlike statements regarding arithmetic have spe-cial verification conditions, there is no reason to suppose that they are specialstructurally.

� Regarding the comment on (11):

� It is easily modifiable so that a hidden quantifier is impossible:

(12) At least two cabinet members oversee every government department,and Tony Blair does too.


� It is also easy to construct pairs of otherwise identical sentences that alternate be-tween a stage- and individual-level predicate, such that both sentences allow inversescope readings:

Context:The speaker is talking about a prestigious annual dinner; at the latest dinner,each table was served by not just one, but several waiters and in fact the chefmade the rounds of the tables, too. Furthermore, this dinner has been held atthe same restaurant several times.

(13) Several waiters served at every table. Chef Pierre did too.(serve � stage-level)

(14) Several waiters knew every customer. Chef Pierre did too.(know � individual-level)


2.3 Need for a Preference Mechanism

� Fox’s theory:

� Too strong

� Other theories that simply allow both surface and inverse scope:

� Too weak

� While not impossible, it is hard to give an inverse scope reading to a source ifthe parallel element in the target is a name.

� What is required:

� A principled way of calculating preferences for interpretation.

� The surface scope readings for sentences like (2) are preferred over inversescope readings.

� Inverse scope readings are nonetheless generally available.

� Asher et al. (1997, 2001) also discuss the need for preferences; we compareour approach to theirs in section 4.4.

� We will account for parallelism possibilities and preferences within GLUE theory:� The linear logic derivations that GLUE uses for semantic composition provide

an appropriate level on which to define parallelism preferences.


3 Glue Proofs: A Level of Semantic Representation

3.1 Identity Criteria for Proofs

� Proof theory: logical proofs are interesting objects in their own right.

� In addition to whether conclusion � follows from premises

� How does it follow?

� Can it follow in more than one way?

� Proofs need interesting, non-trivial identity criteria in order to be regarded asfirst class objects.

� We do not have direct access to the underlying proof objects.

� All we have are marks on paper, i.e. derivations, showing how proofs can berepresented in a particular formal system such as natural deduction.

� What is required: a way of showing how syntactically distinct derivations canbe mapped onto a canonical representation corresponding to the underlyingproof.

� For the fragment of linear logic used in GLUE, there are two convergent ways ofstating the required identity criteria:

1. The Curry-Howard isomorphism (Howard 1980)

2. Proof normalization (cut elimination) (Prawitz 1965)

� Question: How many distinct ways can we derive

�

from

� � �

and

�

?Answer 1: Infinitely many (non-normal form proofs)Answer 2: One (normal form proof)


� Two possible proofs, one canonical (or in normal form) and the other not:

(15)

� � � ��

� � � � � � ��

��

� Derivation 2 introduces a “detour”: it eliminates the implication

� � �

only toimmediately re-introduce exactly the same implication.

� Derivation 1 avoids the detour.

� Proof normalization provides a set of rules for expunging such detours from aderivation

� Derivation 2 is normalized to derivation 1 (

�

-normal form).

� If the formulas in the two derivations above are paired with proof terms via theCurry-Howard isomorphism, we obtain the following

(16)��

� ��

��

�� ! � � � � � � � �� ! � � � � � � � � � �

� The two resulting

�

-terms, � � � � and

� �"�! � � � � � � � � , are equivalent(via

�

- or #-reduction)

� Proof normalization and the Curry-Howard isomorphism converge: normalizing aproof corresponds to

�

-reducing its proof term.

� It is the existence of these normalization / reduction techniques that lead tointeresting identity criteria for proofs.

� We can view normal form derivations as standing for the underlying proofs.


3.2 Identity Criteria for Semantic Compositions

�

GLUE: semantic composition modeled as linear logic proof

� Identity criteria for proofs � identity criteria for semantic compositions.

� We can therefore regard semantic compositions as first class objects in linguis-tic theory, separate from but linked to

1. Syntactic structures2. Model theoretic interpretations

� The modularity of GLUE with regard both to the syntactic framework and tothe meaning language indicates thatGLUE proofs are a way of reifying the syntax-semantics interface.

� Composition as a level of semantic representation goes against the direct model-theoretic interpretation approach of Montague (1970):

� Nothing should sit between syntactic structure and model-theoretic interpreta-tion.

� Composition as a level of representation also goes against the perspective of muchwork in Categorial Grammar and Type-Logical Semantics, which otherwise shareswith GLUE the use of the Curry-Howard isomorphism.

� CG/TLS: no real level of syntactic structure, beyond categorial derivations.

�

GLUE allows for both syntactic structure and model-theoretic interpretation,with a significant level of representation in between.

� Claim: this level of representation is the level for stating parallelism phenomena inellipsis.


3.3 Reconstruction and Parallelism in Semantic Composition

� Basic intuition about ellipsis:the source material is reconstructed in some way so as to make the minimal changesnecessary to incorporate the explicit parallel material in the target.

� Theories differ as to whether ellipsis interpretation is conditioned by

Syntax(e.g, Fiengo and May (1994), Fox (2000) among others)

Semantics(e.g., Dalrymple et al. (1991), Hardt (1993, 1999), Shieber et al. (1996), Asheret al. (1997, 2001), among others)

Both(e.g, Lappin (1996), Merchant (2001), among others)

� An attractive option: ellipsis resolution at the level of the syntax-semanticsinterface


4 Parallelism and Scope in Ellipsis Resolution

� Ellipsis interpreted by taking the source derivation and replacing source premisesby corresponding target premises.

� Yields a target derivation that differs minimally from the source derivation onlyinsofar as it is necessary to incorporate the new target premises.

� Predicts exact scope parallelism in the case of overt quantified NPs in both sourceand target (e.g. Canadian Flag sentences, section 4.1)

� Allows both surface and inverse scope in cases where a non-quantificational NP inthe target is matched by a quantificational NP in the source.

� However: to maximize the degree of parallelism between source and targetderivations, there is a preference for the quantified NP to scope wide (sec-tion 4.2).

� Parallelism is symmetric: also allows both surface and inverse scope in caseswhere a non-quantificational NP in the source is matched by a quantificationalNP in the target (section 4.3).

� Related approaches:

� Our approach is inspired by the equational approach of Dalrymple et al. (1991)and the earlier GLUE approach of Crouch (1999), which used constraints todescribe derivations.

� The constraint/description approach is also shared by the work on ellipsis inthe Constraint Language for Lambda Structures (CLLS) framework (Egg et al.to appear, Egg and Erk 2002, Erk and Koller 2001).

� Asher et al. (1997, 2001) also argue for a preference ordering, but their theoryof parallelism is quite different (section 4.4).


4.1 Quantifier-Quantifier Parallelism

� Consider the Canadian Flag example (4):

(4) A rhino sat in every corner. An elephant did, too.

� The premises for the source sentence are:

(17)

�$ % ��& '() *!+ $ � � ��, � - � � -

. (/ -

() � ' � , � 0

� 1 23 2&4 ��5 *& ) 2& + 1 � � � ' � 6 � � 6

� Two possible normal form derivations:

(18) Surface Scope Source (

78

)

��9 � : � � :�; � < � � <

�9 � =�; � � ; � 9 � >

9 � >

>

� �� ; � >

>

� �� =9 � >

>

(19) Inverse Scope Source (

8 7

)

�; � < � � <��9 � : � � :

�9 � =�; � � ; � 9 � >

9 � >

>

� �� =9 � >

>

�� ; � >

>


� Semantic derivation of the target sentence obtained by replacing the source subject’spremise with the target subject’s premise:

(20)

�$ % � 2 ? 2@ ' %) / + $ � � �, � - � � -

� All instances of , in the source derivation are replaced by ,

in the target derivation.

� With these minimal changes to the source derivation to obtain a target derivation,we obtain exact scope parallelism between source and target.

� Whichever of surface or inverse scope is chosen for the source, the same choicewill be imposed on the target.


4.2 Quantifier-Name Parallelism

� Now consider sentences like (2), which prefer surface scope due to the subject ofthe target being a proper name:

(2) A rhino sat in every corner. Babar did, too.

� The surface and inverse scope derivations for the source sentence in (2) were justshown in (18) and (19).

� We replace the premise for a rhino in the source derivation with the premise forBabar (the parallel element in the target):

(21)

A % A %& � ,

� Depending on which of the surface or inverse scopings ((18) or (19)) are chosen forthe source, this replacement leads to two target derivations

(22) Target from Surface Scope Source (

7 8

)

A % A %& � 9 �; � < � � <

�9 � =�; � � ; � 9 � >

9 � >

>

�� ; � >

>

� �� =9 � >

>

(23) Target from Inverse Scope Source (

8 7

)

�; � < � � <A % A %& � 9

�9 � =�; � � ; � 9 � >

9 � >

>

�� =9 � >

>

�� ; � >

>

� Neither of these derivations is in normal form.


� Eliminating all detours to reduce the derivations to their canonical form shows thatthe two derivations correspond to the same underlying proof:

(24) Normalized target (scopally unambiguous)

�; � < � � <A % A %& � 9

�; � � ; � 9 � >

9 � >

>

�� ; � >

>


� Comparing derivation (24) to the surface scope source reading in (18), we can seethat (24) is a subproof of (18), as indicated in bold.

� By contrast, when we compare (24) to the inverse scope source reading in (19), wesee that the proofs diverge after the third line.

(24) Normalized target

�B � C � � CA % A %& � D

�B � E B � D � F

D � F

F

�� B � F

F(18) Surface Scope Source (

78

)

��9 � : � � :�B � C � � C

� D � G�B � E B � D � F

D � F

F

�� B � F

F

�� =9 � >

>

(19) Inverse Scope Source (

8 7

)

�; � < � � <��9 � : � � :

� D � G�B � E B � D � F

D � F

F

�� =9 � >

>

�� ; � >

>


� (24) and (18) are parallel to a greater degree than (24) and (19) are

� The surface scope reading for the source sentence in (2) is the preferred read-ing.

� Either surface or inverse source scoping is permissible on the GLUE approach,both leading to a scopally unambiguous target derivation.

� However: in terms of maximizing the degree of parallelism between sourceand target derivations, there is a preference for the source to have surfacescope, where the quantified subject scopes wide.

� The calculation of degree of parallelism must compare normal form deriva-tions.

� It is the underlying proofs that need to be compared, not the way in whichthey happen to be written down (with or without detours).


4.3 Name-Quantifier Parallelism

� What happens when a non-quantified source subject is replaced by a quantifiedtarget subject, as in

(25) Babar sat in every corner. A rhino did, too.

� We predict that either scoping is available for the target, but with a preferencefor surface scope / wide scope subject.

� The (normal form) source derivation is unambiguously

(26) Source derivation (scopally unambiguous)

�; � < � � <A % A %& � 9

�; � � ; � 9 � >

9 � >

>

�� ; � >

>

� It might appear that we can replace the source premise

A % A %& � , with the targetpremise� $ % ��& ' () *!+ $ � � �, � - � � -

� This replacement is misleadingly straightforward.� It relies on the fact that we just happened to represent the verb premise as

(27)

�4 �"H . 2 2 � H + 4 � � ' � , � 0

� We could just as easily have written an equivalent premise by Currying the function

(28)

�H �4 . 2 2 � H + 4 � � , � ' � 0

in which case the source derivation would have been

(29)

�; � < � � <A % A %& � , 9 � ; � >

; � >

>

� In this essentially equivalent derivation, it is not obvious how to replace 9

by

��9 � : � � :

to produce a valid derivation.


� There is a difference between

1. Replacing a source quantifier by a target name, and

2. Replacing a source name by a target quantifier

� Case 1 works out easily because a name GLUE constructor such as 9 alwaysentails the corresponding quantifier constructor

��9 � : � � :

, as the fol-lowing (type raising) derivation shows

(30)

� "� 9 � � � � I� 9

�� I � � �

�� I � � ��9 � � � � �

� Notice that type raising follows purely from the proof rules, without furtherstipulation.

� This means that whenever we want to replace a quantifier by a name, we alwayshave the option of type raising the name to a quantifier and replacing it directly.

� But for case 2 the reverse entailment does not hold: a quantifier constructor cannotbe type-lowered to entail a name constructor.

� A general mechanism for replacing a name by a quantifier therefore must

1. Replace the name premise by an assumption, and

2. At some suitable point in the derivation discharge this assumption and intro-duce the quantifier premise


� This leads to the following two target derivations from (26)

(31) Surface Scope Target (

7 8

)

��9 � : � � :�; � < � � <

�9 � =�; � � ; � �9 � > �

9 � >

>

� �� ; � >

>

�� =9 � >

>(32) Inverse Scope Target (

8 7)

�; � < � � <�9 � : � � :

�9 � =�; � � ; � �9 � > �

9 � >

>

�� =9 � >

>

�� ; � >

>

� Normalizing the surface and inverse scope target derivations, and comparing to thenormalized source derivation reveals that the surface scope target displays a greaterdegree of parallelism to the source.

1. (26) is a subproof of (31)(compare (24) and (18) above)

� The preference for a quantifier replacing a name to scope wide is independent ofthe way in which we happen to write the verb premise down.

� Parallelism is symmetric:

1. A proper name subject in the target leads to preference for surface scope source.

2. A proper name subject in the source leads to preference for surface scope target.


4.4 Implications of the Theory

� The amount of overlap between ellipsis source and target derivations determineswhich scope readings are preferred.

� The preferred reading is the one that maintains maximum overlap.

� This contrasts with theories that allow inverse scope just as easily as surfacescope.

� We are not ruling out inverse scope on the basis of the availability of surface scope.

� This contrasts with Fox’s economy approach.

� Asher et al. (1997, 2001) also consider ellipsis, scope, and parallelism and state theneed for a preference ordering on scope readings.

� Similarities:

� Use of a logical form (Segmented Discourse Representation Structures)

� Preference ordering

� Symmetric parallelism (source/target)

� Differences:

� No normal form proposed for logical forms

� Specific parallelism between names and wide scope existentials

� Further modifications to the theory required to handle general scope paral-lelism

5 Conclusion

1. Semantic derivations are a useful and interesting level of linguistic representation.

� But, require strong identity criteria (normalization procedure)

2. Semantic derivations are the proper locus for calculating ellipsis parallelism.

�

GLUE derivations allow statement of a preference ordering.

� General preference for a quantifier that is parallel to a name to scope wide.


References

Asher, Nicholas, Daniel Hardt, and Joan Busquets (1997). Discourse parallelism, scope,and ellipsis. In Aaron Lawson (ed.), Proceedings of SALT VII.

Asher, Nicholas, Daniel Hardt, and Joan Busquets (2001). Discoure parallelism, ellipsis,and ambiguity. Journal of Semantics, 18.

Crouch, Richard (1999). Ellipsis and glue languages. In Shalom Lappin and ElabbasBenmamoun (eds.), Fragments: Studies in ellipsis and gapping.

Dalrymple, Mary (ed.) (1999). Semantics and syntax in Lexical Functional Grammar:The resource logic approach. Cambridge, MA: MIT Press.

Dalrymple, Mary (2001). Lexical Functional Grammar. San Diego, CA: AcademicPress.

Dalrymple, Mary, Stuart M. Shieber, and Fernando C. N. Pereira (1991). Ellipsis andhigher-order unification. Linguistics and Philosophy, 14, 399–452.

Egg, Markus, and Katrin Erk (2002). A compositional account of VP ellipsis. In Frankvan Eynde, Lars Hellan, and Dorothee Beermann (eds.), Proceedings of the HPSG ’01conference, Stanford, CA. CSLI Publications.

Egg, Markus, Alexander Koller, and Joachim Niehren (to appear). The Constraint Lan-guage for Lambda Structures. Journal of Logic, Language, and Information.

Erk, Katrin, and Alexander Koller (2001). VP ellipsis by tree surgery. In Proceedings ofthe 13th amsterdam colloquium, Amsterdam.

Fiengo, Robert, and Robert May (1994). Indices and identity. Cambridge, MA: MITPress.

Fox, Danny (1995). Economy and scope. Natural Language Semantics, 3, 283–341.Fox, Danny (2000). Economy and semantic interpretation. Cambridge, MA: MIT Press.Hardt, Daniel (1993). Verb phrase ellipsis: Form, meaning, and processing. Ph.D. thesis,

University of Pennsylvania.Hardt, Daniel (1999). Dynamic interpretation of verb phrase ellipsis. Linguistics and

Philosophy, 22, 185–219.Hirschbuhler, Paul (1982). VP-deletion and across-the-board quantifier scope. In James

Pustejovsky and Peter Sells (eds.), Proceedings of NELS 12, (pp. 132–139), Universityof Massachusetts, Amherst. GLSA.

Howard, William A. (1980). The formulae-as-types notion of construction. InJonathan P. Seldin and J. Roger Hindley (eds.), To H.B. Curry: Essays on combinatorylogic, lambda calculus and formalism, (pp. 479–490). London: Academic press.

Jacobson, Pauline (1998). Where (if anywhere) is transderivationality located? In LouiseMcNally and Peter W. Culicover (eds.), The limits of syntax, (pp. 303–366). San Diego,


CA: Academic Press.Johnson, David, and Shalom Lappin (1997). A critique of the Minimalist Program.

Linguistics and Philosophy, 20, 273–333.Johnson, David, and Shalom Lappin (1999). Local constraints vs. economy. Stanford,

CA: CSLI Publications.Kratzer, Angelika (1989). Stage-level and individual-level predicates. In Emmon Bach,

Angelika Kratzer, and Barbara Hall Partee (eds.), Papers in quantification. Amherst,MA: University of Massachusetts, Amherst.

Kratzer, Angelika (1995). Stage-level and individual-level predicates. In Gregory N.Carlson and Francis Jeffry Pelletier (eds.), The generic book. Chicago: University ofChicago Press.

Lappin, Shalom (1993). Ellipsis resolution at S-structure. In A. J. Schafer (ed.), Pro-ceedings of NELS 23, (pp. 255–269), University of Massachusetts, Amherst. GLSA.

Lappin, Shalom (ed.) (1996). The handbook of contemporary semantic theory. Oxford:Blackwell.

Merchant, Jason (2001). The syntax of silence. Oxford: Oxford University Press.Montague, Richard (1970). English as a formal language. In Bruno Visentini et al. (eds.),

Linguaggi nella societa e nella tecnica, (pp. 189–224). Milan: Edizioni di Communita.Reprinted in (Montague 1974:188–221).

Montague, Richard (1973). The proper treatment of quantification in ordinary English.In Jakko Hintikka, Julian Moravcsik, and Patrick Suppes (eds.), Approaches to lan-guage, (pp. 221–242). Dordrecht: D. Reidel. Reprinted in (Montague 1974:247–270).

Montague, Richard (1974). Formal philosophy: Selected papers of Richard Montague.New Haven: Yale University Press. Edited and with an introduction by Richmond H.Thomason.

Prawitz, Dag (1965). Natural deduction: A proof-theoretical study. Stockholm:Almquist and Wiksell.

Sag, Ivan A. (1976). Deletion and logical form. Ph.D. thesis, MIT.Shieber, Stuart M., Fernando C. N. Pereira, and Mary Dalrymple (1996). Interactions of

scope and ellipsis. Linguistics and Philosophy, 19, 527–552.Williams, Edwin (1977). Discourse and logical form. Linguistic Inquiry, 8, 101–139.

Issues in Resource Management

NASSLLI 2001The Syntax-Semantics Interface

Ash Asudeh, Dick Crouch, Mary Dalrymple

Introduction

� Resource-sensitive theory of the syntax-semantics interface:theoretical and computational advantages.

� Interesting tension arises

– Resource deficit

� Theoretical: multiple consumers for a resource� Empirical: control, coordination, right node raising, serialverbs, noun incorporation

– Resource surplus

� Theoretical: no consumer for a resource� Empirical: control, resumptive pronouns, copy raising

2

Not enough resources: resource deficit

� Resource deficit in GLUE:multiple consumers for a single resource (consumption target)

� � � � � � � � � � ��

� � � � � � � � � � � � �

� Correlates with f-structure identity(f F )� (f F � )

f �

F g ��

F ��

�

3

Resource deficit: the general solution

� One consumer (principal consumer ):

1. Consumes the other consumers (subsidiary consumers)2. Handles the meanings of the subsidiary consumers appro-

priately3. Consumes the consumption target and distributes its mean-

ing accordingly

� A schematic example:

Consumption target ��

Subsidiary consumers � � � � �

� � � � �

Principal consumer � � � � ��

4

Example 1: Control

(1) Gonzo attempted to sneak off.

a

! """"""#

PRED ‘attempt’

SUBJ g $ PRED ‘Gonzo’ %XCOMP s &

PRED ‘sneak off’

SUBJ '( ))))))*

Gonzo ( + PRED), ‘gonzo’-./0 . : +1, -

sneak off ( + PRED), ‘sneak off’234 5/67 8 -. 9 :3 ; : ( + SUBJ)1< +1, -< 5

attempted=>? =@ >A BC ?D =E @D @F A ( + PRED), ‘attempt’( + SUBJ), ( + XCOMP SUBJ)2G 2347 H H6I J H :3 K ˆG ; : (( + XCOMP SUBJ)1< ( + XCOMP)1 )< (( + SUBJ)1< +1 ), : -< 5 ;< : -< 7 ;

attempted=>? =?LM AM ? F C ?D =E @D @F A ( + PRED), ‘attempt’( + SUBJ), ( + XCOMP SUBJ)2G 2347 H H6I J H :3 K ˆG :3 ; ; : (( + XCOMP SUBJ)1< ( + XCOMP)1 )< (( + SUBJ)1< +1 ), : -< 5 ;< : -< 7 ;

5

Example 2: Coordination

N Coordination rule from syntax (similar to GPSG, CCG):X O XP CONJ XN Coordination as modificationN Coordination schema in semantics (similar to Type Logical Semantics):

QRS R T UWV X Y[Z \] ^ Z UV X Y Z \_ ^

QR Q ` Q V aS bR U V a ^c ` U V a ^d T UeV X YfZ \g ^ Z U UeV X YfZ \_ ^ Z UeV X YfZ \_ ^ ^N E.g: S-coordination h Xi j , VP-coordination h X i subject, etc.

(2) Kim slept and dreamt.

QRS R T Ulk Z m ^ Z Ulk Z n ^QR Q ` QoS bR Uo ^ c ` Uo ^d T Ulk Z p ^ Z U Ulk Z n ^ Z Uk Z n ^ ^

qrstu v wx qy z{ z v | wx q }x | wx ~ }qrstu v wx ~ ��s s � v wx �y zy �y �{ � z | � }� � | � }� v | wx � }x | | wx ~ }x | wx ~ } }y �y �{ � ��s s � | � } � � | � }� v | wx ~ }x | wx ~ }y �{ � ��s s � | � } � qrstu | � }� v wx ~ w�u v w� ��s s � | w�u } � qrstu | w�u }� v ~

6

Too many resources: resource surplus

� Resource surplus in GLUE:an extraneous resource (for semantic composition)contributed by the syntax� � � � ��

� A common situation:the extraneous resource is an orphan because its consumerhas been consumed

� � �� ’ p� � � p��

� � � � � � � � � � � � � � �

7

An observation about resource surplus

� In empirical phenomena that involve resource surpluses, theextraneous resource is

– An orphan– An anaphoric element (pronoun or epithet)

� This would seem to indicate that whatever deals with resourcesurplus must deal with a resource/premise contributed by ananaphor.

8

Resource surplus: the general solution� Manager resources are contributed by some lexical item in the

environment of the orphan resource.

� The manager resource consumes the orphan resource, dis-pensing with its semantic contribution, which is extraneous bydefinition.

� Since the orphan resource is anaphoric, the result of this con-sumption is a modifier on the antecedent.

� A schematic example:

Antecedent ��

Anaphor (orphan) �� Manager resource � � ��

9

Example 1: Irish resumptive pronouns

� The complementizers in Irish inflect roughly as follows (McCloskey 1979, Sells 1984):

– go: neutral complementizer

– aL : indicates a gap (induces lenition mutation)

– aN : indicates a resumptive pronoun (induces nasalization mutation)� aN indicates a resumptive pronoun in the material it introduces

(3) anthe

ghirseachgirl

a-raN-PAST

ghoidstole

nathe

sıogaıfairies

ıher

‘the girl that the fairies stole away’(McCloskey to appear:7, (9b))� The resumptive need not be in the clause immediately introduced by aN .� There must be a pronoun below aN ; it cannot introduce a clause with a gap.

(4) * anthe

bheanwoman

aaN

bhfacasaw

SeanS.

‘ the woman that John saw’(McCloskey to appear:20, (45b))� The resumptive pronoun need not be the first suitable pronoun below aN .

10

F-structure for (3)

(5)

g

� ��

PRED ‘girl’

PERS 3

NUM SG

SPEC � PRED ‘the’ �

ADJ

� ��

s

� ��

PRED ‘steal’

SUBJ f

� ��

PRED ‘fairy’

PERS 3

NUM PL

SPEC � PRED ‘the’ ��

OBJ p

� ��

PRED ‘pro’

PERS 3

NUM SG

GEND FEM

PRONTYPE PERS

� ��

TOPIC

TENSE PAST

� �� ¡ ��¢��£

� ��

11

Relevant lexical entries

aN ( ¤ TOPIC) ¥f¦ (( ¤ GF§ ) ¥ ANTECEDENT)

¨© ¨ª« ª : [( ¤ TOPIC) ¥¬ (( ¤ TOPIC) ¥ ( ¤ GF§ ) ¥ )]¬

(( ¤ TOPIC) ¥¬ ( ¤ TOPIC) ¥ )¦ ®¯ ¬ ®¯ ° ± ± ¬ ®¯ ¬ ¯ ±

¨© ¨ ² ¨ª« © ®ª ±³ ² ®ª ± : [( ¤ TOPIC) ¥¬ ¤ ¥ ]¬

[[((ADJ ´ ¤ ) ¥ VAR)¬ ((ADJ ´ ¤ ) ¥ RESTR)]¬

[((ADJ ´ ¤ ) ¥ VAR)¬ ((ADJ ´ ¤ ) ¥ RESTR)]]¦ ® ° ¬ µ ± ¬ ® ®¶ ¬ · ± ¬ ®¶ ¬ · ± ±

ı ( ¤ PRED)¦ ‘pro’( ¤ PERS)¦ 3( ¤ NUM)¦ SG

( ¤ GEND)¦ FEM

¨ ¸« ¸¹ ¸ : ® ¤ ¥ ANTECEDENT ± ¬ ® ® ¤ ¥ ANT ± ¤ ¥ ±¦ ¯ ¬ ®¯ ° ±ghoid ( ¤ PRED)¦ ‘steal’

( ¤ TENSE)¦ PAST¨ ¸ ¨ª« µº»¼½ ®ª ¾ ¸ ± : ® ¤ OBJ ± ¥ ¬ ® ¤ SUBJ ± ¥ ¬ ¤ ¥¦ ° ¬ ¿ ¬ µ 12

GLUE derivation for (3)À< Á

ÂÃÄÆÅ Ã< Ç< ÈÇ< È ÉÊ 4 : Ç< Ê ;< Ê Ê , ÈÈ Ë Ì Í ÎÅÃ< È : Ã< È ;< : : À< Á ;< : À< Á ; ;: À< Á ;< : À< Á ;À< Á : À< Á ;< ÉÏ 4 :Ð < Ï ;< ÏÉÏ 4 :Ð < Ï ;< Ï

Ð < :ÐÑ Ã; :Ð < :Ð Ñ Ã; ;< :Ð < Ð ;Ð < Ð ÂÐ ÄÓÒÐ ÂÐ < Ô ÄÖÕÔ Ë Ì Í ÎÒÐ < Ô ÉÏ 4 :Ð < Ï ;< Ï Ï , ÔÔ Ë Ì Í ÎÕ:Ð < Ô ;< Ô É Í2 G 4 H×6 :Ø K H ×6 :3 K Ù7 YÚ Ø * :3 ; K 5 H6 7 Û :3 K Ø ; ;Ü - YÚ Û : Ø ; KG :Ø ; ;Ý ÉÞ 4 : -< Þ ;< Þ

13

Example 2: Copy raising

(6) Richard seems like he exercises.

(7) Richard seems like Kim has dumped him.

(8) Nobody seems like he failed.

(9)

s

ß ààààààààààààààààààààá

PRED ‘seem’

SUBJ

XCOMP l

ß ààààààààààààààá

PRED ‘like’

SUBJ r â PRED ‘Richard’ ã

COMP e

ß àààààààá

PRED ‘exercises’

SUBJ p

ß ààààá

PRED ‘pro’

PERS 3

NUM SG

GEND MASC

ä ååååæ

ä åååååååæ

ä ååååååååååååååæ

ä ååååååååååååååååååååæ

14

Lexical entries for (6)

Richard ·ç : ¤ ¥¦ ·

exercises ¨ª« » ª » · ®ª ± : ( ¤ SUBJ) ¥¬ ¤ ¥¦ ° ¬ »

he ¨ ¸« ¸¹ ¸ : ® ¤ ¥ ANTECEDENT ± ¬ ® ® ¤ ¥ ANTECEDENT ± ¤ ¥ ±¦ · ¬ ® · ° ±

like ¨è © ¨ª«½ éê » ®ª ¾ ˆè © ± : ® ¤ COMP ± ¥ ¬ ® ¤ SUBJ ± ¥ ¬ ¤ ¥¦ » ¬ · ¬ ½

seem ¨ª ¨© « µ» »ë ® ˆ© ®ª ± ®ª ± ± : ® ¤ SUBJ ± ¥ ¬ì ® ¤ GF§ ± ¥ ¬ ® ¤ XC SUBJ ± ¥ ¬ ® ¤ XC ± ¥ í¬ ¤ ¥¦ · ¬ ® ° ¬ · ¬ ½ ± ¬ µ

¨ © ¨ª« ª : ì ® ¤ SUBJ ± ¥ ¬ ® ® ¤ SUBJ ± ¥ ® ¤ GF§ ± ¥ ± í¬® ® ¤ SUBJ ± ¥ ¬ ® ¤ SUBJ ± ¥ ±¦ ® · ¬ ® · ° ± ± ¬ ® · ¬ · ±� Meaning postulate: î è © î ª«½ éê » ®ª ¾ ˆè © ±ï ð© « ˇ© ®ª ±³ñ ® ˇè © ï ˇ© ®ª ± ±

15

GLUE derivation for (6)

b � dóò � Z �� Z � Z ô� Z ô Ë Ì Í ÎÅ� Z � Z ô

õ Z U õ ö ÷ ^ U õ Z U õ ö ÷ ^ ^ Z U õ Z õ ^õ Z õ ��

� � Z U � Z � Z ô ^ Z pU � Z � Z ô ^ Z p � Z � Z ôp � �� U ˆôø k � U� m ù ˆ�o �� U� m ^ ^ ^ T p16

Further reading� Resource deficit

– Right node raising: Kehler et al. (1999), Asudeh (2000a)– Coordination: Asudeh and Crouch (2002)– Control: Asudeh (2000b, 2002)– Raising: Asudeh (to appear), Asudeh (in prep)

� Resource surplus

– German split NPs: Kuhn (2001)– Copy raising: Asudeh (to appear), Asudeh (in prep)– Resumptive pronouns: Asudeh (in prep)– Control: Asudeh (2000b, in prep)

17

References

Asudeh, Ash (2000a). Functional identity and resource-sensitivity in control.Handout for talk given at the LFG ’00 conference, Berkeley, CA. Available athttp://www.stanford.edu/ ú asudeh.

Asudeh, Ash (2000b). Functional identity and resource-sensitivity in control.In Miriam Butt and Tracy Holloway King (eds.), Proceedings of the LFG ’00conference, Stanford, CA. CSLI Publications.

Asudeh, Ash (2002). A resource-sensitive semantics for equi and raising. InDavid Beaver, Stefan Kaufmann, Brady Clark, and Luis Casillas (eds.), Theconstruction of meaning. Stanford, CA: CSLI Publications.

Asudeh, Ash (in prep). Resumption as resource management. Ph.D. thesis,Stanford University.

Asudeh, Ash (to appear). Richard III. In CLS 38: The main session.

Asudeh, Ash, and Richard Crouch (2002). Glue Semantics for coordination:Reconciling discourse cohesion and the element constraint through proofparallelism. Handout for talk given at Semfest 3, Stanford, CA. Available athttp://www.stanford.edu/ ú asudeh.

18

ReferencesKehler, Andrew, Mary Dalrymple, John Lamping, and Vijay Saraswat (1999).Resource sharing in glue language semantics. In Mary Dalrymple (ed.), Se-mantics and syntax in Lexical Functional Grammar: The resource logic ap-proach, (pp. 191–208). Cambridge, MA: MIT Press.

Kuhn, Jonas (2001). Resource sensitivity in the syntax-semantics interfaceand the German split NP construction. In W. Detmar Meurers and TiborKiss (eds.), Constraint-based approaches to Germanic syntax . Stanford, CA:CSLI Publications.

McCloskey, James (1979). Transformational syntax and model theoretic se-mantics: A case-study in Modern Irish. Dordrecht: Reidel.

McCloskey, James (to appear). Resumption, successive cyclicity, and the lo-cality of operations. In Samuel Epstein and T. Daniel Seeley (eds.), Prospectsfor derivational explanation. Oxford: Blackwell.

Sells, Peter (1984). Syntax and semantics of resumptive pronouns. Ph.D.thesis, University of Massachusetts, Amherst.

19

Modifiers and Glue Proof Search

and

Glue for Other Grammatical Frameworks

NASSLLI’02Syntax-Semantics Interface

Friday 28th June

Recap on Modifiers

� Semantic modifiers correspond to � � � � glue identitiesQualifications:— Dependent modifiers like quantifiers: ��

— Other impure but purifiable modifiers

� Semantic ambiguity arises through different interpolations of � � � �

modifiers around � skeletons.

� Investigate proof search strategies exploiting modifier structure of gluederivations— Sketch why modifiers are important to efficient glue implementation— Superficial overview only

Goals of Glue Proof Search

� � � �

� Find all possible proofs of sentence meaning � � � from premises

� Multiple derivations from single premise set invariably due to multiplemodifier interpolations— Empirical observation about linguistically natural glue premises

� Use of packing / structure sharing— �� analyses from permutation of � sub-analyses

— Compute each sub-analysis once— Polynomial computation and representation of permutations— Linear time (backtrack-free)read out for any given analysis— Cf. use of charts in parsing

Two-Step Derivations

� Suppose all premises were either pure skeleton, pure modifier or (re-arranged) purifiable modifier.

� Two stage derivation:1. Initial derivation separating modifiers from skeleton

��

�

� � � � � � � � ��

skeleton

� � � � � � � � � �� pure modifier

� �� pure modifier

Typically linear time: usually just one +ve and –ve skeleton occurrence of eachatom

2. Final derivation inserts modifiers

Inserting modifiers� ��

� � ��

�

+

� ��

�

� ��

� ��

� � �

� ��

Determine if there is a valid proof while ignoring pure modifiers

Inserting a pure modifier can’t make a valid proof invalid

Efficiency from Modifier Insertion

Modifier insertion: more efficient structure sharing than charts.Consider example from parsing

S

NP VP

John V SComp

said that S

NP VP VP� � VP

Bill left yesterday

— Skeleton-modifier approach:Skeleton structure built just once

— Chart approach: disjointness conditions on string spansSkeleton structure has to be built twice— once with low modifier attachment, once without

Significant computational pay-off from modifier insertion

Non-Purifiable = Dependent = Non-Horn

� A quantifier, like � � � � � � � , is non-purifiable— Cannot separate �� into a skeleton prefix and a modifier suffix.— Cannot straightforwardly carry out first skeletal derivation stage.

i.e. cannot match skeleton prefix to get pure modifier

� � � � � � � � , is also a dependent modifier.— It modifies an that is missing / dependent on a � , to give an where the

dependency has been discharged.— The� has a free variable meaning � that gets bound when the dependency is

discharged

� Non-purifiable modifiers are also non-Horn clauses— Horn clause: ��

Atom, or implication from an atom to a Horn clause.

Horn Clause Compilation (Hepple 96)

Compile non-Horn formula � � � � � � �

to pair of Horn formulas �� , � � ��

where

� �� (uniquely indexed) assumption of�

� � � �� is just � � � � — except that�� must be used in deriving �

Example Proof Rule� � � � � � �

��

� � � � ��

�

�! � � �� "# $%

...

� ! �

� �& � � �! �

Example: “Someone slept”

� Uncompiled Premises: � Compiled Premises:

��

� � ��

��

� Two step derivation:Skeleton Modifier Result

� � � � ��

+ � � � ��

� � � � ��

�

� Note that insertion of dependent modifiers must make non-local checkon derivation tree to ensure that dependency has actually been used.

Approaches to Glue Inference

� Hepple (96, 98):— Horn clause compilation— Chart-based theorem proving without reference to modifier structure

� Gupta & Lamping (98):

— Partial Horn clause compilation to separate skeletons and modifiers— Leave insertion of modifier underspecified

� Combination:— Pack the insertion of modifiers into the skeleton

Summary

� Glue enables a precise, formal definition of semantic modifiers

� The definition is linguistically natural

� It is also a key computational insight— See how far glue for other grammatical frameworks preserves this insight

Glue for other Grammatical Frameworks

Glue: General Theory of Semantic Composition� Applies to wide range of linguistic phenomena

E.g.: quantifier scope, intensionality, control, coordination, anaphora, . . .

(Dalrymple et al 97, Asudeh 00, Crouch & van Genabith 99)

� Applies to wide range of semantic representationsE.g.: Montague’s IL, (C)DRT, UDRT

(Dalrymple et al 97, van Genabith & Crouch 99, Crouch et al 01)

� Applies to wide range of grammatical formalismsE.g.: LFG, HPSG, CFG, CG, LTAG, DTG, . . .

Glue for HPSG (Asudeh & Crouch 2001)Kim walked

S

��

CAT ��

HEAD � TAG � �

VALENCE � SUBJ � �

�

CONT � GLUE kim: � ( � ), walk : � ( � ) � � � ( � ) � �

�

NP VP

� ��

CAT � HEAD � TAG � �

CONT � GLUE kim: � ( � ) � �

�

��

CAT

��

HEAD � TAG � �

VALENCE � SUBJ � � NP � TAG � � �

�

CONT � GLUE walk : � ( � ) � � � ( � ) � �

�

Kim walked

Modifications to HPSG

� New HEAD feature TAG— Gives names to maximal projections of each head— � : maps tags to glue semantic resources— TAG feature passed up by Head Feature Principle

� GLUE feature: value is list (multi set) of glue premises

� SEMANTICS PRINCIPLE (glue version)The GLUE of a phrase is the concatenation of the GLUE values of itsdaughters.

phrase ��

CONT � GLUE � � . . . � � �

DAUGHTERS � � GLUE � � , . . . , � GLUE � � ! """

#

Building a Quantified NP

NP

��

CAT $ HEAD % TAG& '

CONT ��

GLUE (*) P.) Q. + X.[P(X) , Q(X)]:

( -. / 0 ). / ((& . / G). / G),

student : - . / 0 1�

�

Det N2

��

CAT��

�HEAD % TAG tag '

SPEC3 N4 % TAG& ' : �

VAR-TAG -

RESTR-TAG 0 �

�

CONT 5 GLUE 6) P.) Q. + X.[P(X) , Q(X)]:

( - . / 0 ). / ((& . / G). / G) 7 8

�3 ��

�

CAT $ HEAD % TAG& '

CONT ��

GLUE 9 student : - . / 0 :

VAR-TAG -

RESTR-TAG 0 �

�

every student

RESTR-TAG: identifies N-bar resource (cf RESTR for LFG glue)

HPSG vs LFG Glue� Both: lexical, headed, unification-based grammars

� Both: parsing instantiates lexical entries to yield premises

� Both: resulting glue premises broadly similar— Headedness leads to prevalence of modifiers as glue identities

Hence efficient deduction

� LFG: parallel construction of multiple representations— Glue deduction: separate syntactic and semantic construction construction

� HPSG: construction of single, sign-based representation— How to represent results of glue deductions within HSPG sign?

Why Do Glue for HPSG?

Largely a matter of taste

� Other approaches to HPSG semantics are available— e.g. Pollard & Sag 94, MRS, . . .— with similar coverage of phenomena (scope, control, recursive modification, . . . )

� But glue may simplify HPSG feature geometry— e.g. P&S’94 include quantifier storage mechanism in feature geometry

� Glue resources & derivations as rational reconstruction of elementarypredications, labels & scope constraints in MRS.

Glue for Context Free Grammar

� Non-lexical, non-headed, non unification-based grammar

� Glue semantics is possible (but not advisable)

� Premises: not obtained by instantiation of lexical entries

� Premises: different structure to LFG/HSPG counterparts— Non-headedness: semantic modifiers generally not �� identities

Leads to poor computational properties— However quantified NPs still �� modifiers

So quantifier scope ambiguity still handled well

CFG-Glue Fragment

S � NP VP &� � � �� ! ��

VP � V� &� �� ! � ��

VP � V � NP &� � � �� ! � ��

NP � Det N &� �� ! � ��

V� � walks walk! � �

V � � saw see! � �

NP � John ! ��

Det � every &� � � � � �� ! � ��

N � man � � � ! � �

S

NP� VP �John V �

walks��

� � ��

� � �

� � � � �

� � � � � � �

Glue for LTAG (Frank & van Genabith 2001)Substitution

S � � �

NP � � � NP � � �� VP � � � NP � � �

N � � � V � � � NP � � �� N � � �

John meets Mary

��

� � � ��

AdjunctionS � � �

NP � � � � VP � � � VP ��

V � � � NP � � � � Adv VP* ��

John meets Mary often

� � � � � � ��

��

Adjunction �� semantic modification

LTAG keeps long distance dependencies ‘local’ via adjunction

Who does Peter think John meetsS

NP � � [+wh] does S

NP � � VP

meet e

S

NP � � VP

think S*

� Complicates glue labelling scheme— Each node has a consumer (top) and producer (bottom) label

— These labels are set equal in completed derivation trees— Adjunction by modifiers preserves identities— Adjunction by non-modifiers splits identities

Consumer (top) and Producer (bottom) Labels

S ��

NP � � � � � � � �� does S � ��

NP � � � � � � � � � �� VP � � ��

meet e

� ��

Modifier AdjunctionVP ��

often VP* � ��

Non-Modifier AdjunctionS ��

NP � � � � � � � � �� VP � � � �

think S* � ��

Who does Peter think Bob often meets

S ��

NP � � � � � � � �� does S � ��

Who NP � � � � � � � � �� VP � � � �

Peter think S* � ��

NP � � � � � � � � � �� VP � � ��

Bob often VP* � � � � �

meets e

� � � � ��

� � � ��

Adjunction and Modification in LTAG� Superficially, LTAG adjunction looks like Glue modifier insertion

� But extended domains of locality mean that adjoined constituents arenot always semantic modifiers

� Producer and consumer labels on nodes can be used to reconstitutesemantic distinction between modifiers and non-modifiers

� Once this is done, glue premises closely resemble those of LFG andHPSG

� Glue for Derivation-Tree Grammar (Hepple 99): similar to LTAG

Glue for Categorial Grammar

� Lexicalized, non unification-based grammar

� Premises obtained from lexical entries— But not via unification / instantiation— Use Curry-Howard Isomorphism to build sets of premises

� Premises can be made similar to LFG/HPSG counterparts— Hence efficient glue deduction

� Topic has not been investigated in depth

CG-Glue Fragment

Glue terms for Lambek calculus:— Pair of � head-resource, conjunction-of-premises �

— Projections � and � onto head and premises

Word Category Glue Term

John NP � � � john! � �

Fido NP �� fido! � �

saw (NP � S)/NP & � � � � �� see! � � � ��

� � � � � � � � � � �

NP � � � john� �

(NP � S)/NP � � � � � � � see� � � � �� NP � � � fido� �

NP � S � � � � � see� �� fido� � � � � �

S � � � see� �� fido� � � john� �

Syntactic derivation assembles conjunction of glue premises

Glue Semantics and Categorial Semantics

Glue semantics �

Categorial (grammar + semantics) – categorial grammar

— Categorial parsing: deduction in (non-commutative) linear logic— Categorial semantics: directly via Curry-Howard on parse deduction

NP � john

(NP � S)/NP � see NP � fido

NP � S � see � fido �

S � see � fido � � john �

Produces same semantics as previous CG+Glue example.

What’s the point of a second (glue) derivation?

1. CG and Scope� Quantifiers can scope against word order

� Commutativity and word order— Categorial logic = non-commutative linear logic (to account for word-order)

Glue logic = simpler, commutative linear logic (syntax accounts for word-order)

� CG introduces new operator � to relax non-commutativity

�� ! � � � �

� � �

�! � ��

��

� ! � �

�& � � � �! �

Glue requires no additional proof rules

� Question: To what extent is CG+Glue equivalent to CG+ � ?— Philosophical taste: the idea of a syntactic derivation distinct from a semantic

derivation is anathema to categorial grammarian, congenial to glue semanticists

2. CG and Modifiers

� CG has a limited stock of atomic resources: � ��

A resource for each type of grammatical category

� Glue has a richer stock of atomic resources:� ��

A resource for each instance of a grammatical category exemplified in a parse

� CG, like LTAG, does not always clearly identify semantic modifiers:— often: (NP � S) � (NP � S)

— promise: (NP � S) � (NP � S)

� Glue distinguishes different occurrences, and hence genuine modifiersfrom e.g. control verbs— often: (NP � � S � ) � (NP � � S � )— promise: (NP � � S � ) � (NP � � S � )

Finally: Glue

� A general, deductive, resource-based account of the syntax-semanticsinterface— Various semantic representation languages— Various grammatical formalisms

� Elegant accounts of a wide variety of phenomena— Recursive modification, quantification, resumption, ellipsis— Anaphora, coordination, event-based semantics, lexical decomposition, . . .

� Modifiers: linguistic & computational importance

� Glue proofs as genuine levels of semantic representation— Being applied to notions of semantic parallelism, . . .

The Syntax-Semantics Interface: Theory and … · 1 1 A Brief Overview of Glue Semantics and Linear...

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