Glue for Minimalist Syntax Glue Semantics for Minimalist Syntax

Glue semantics (Slides available at http://www.ucl.ac.uk/ ~ucjtmgg/docs/LAGB2015-slides.pdf ) Glue Semantics for Minimalist Syntax ◮ A theory of the syntax/semantics interface. ◮ Matthew Gotham Originally developed for LFG, and now the mainstream view of the syntax/semantics interface within LFG (Dalrymple, 1999). Department of Linguistics ◮ Implementations also exist for HPSG (Asudeh and Crouch, 2002) and University College London LTAG (Frank and van Genabith, 2001). Annual Meeting of the LAGB Key ideas: 18 September 2015 ◮ Syntax+lexicon produces a multiset of premises in a fragment of (Girard, 1987). Slides available at ◮ Semantic interpretation consists in finding a proof to a specified type http://www.ucl.ac.uk/ ucjtmgg/docs/LAGB2015-slides.pdf ~ of conclusion from those premises. (like in )

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax

Aims of this talk Plan for the rest of the talk

◮ To give an implementation of Glue in Minimalism. A fast introduction to Glue semantics ◮ To show that it has some potential advantages over more Linear logic and Glue conventional approaches to the syntax/semantics interface. The fragment to be used What I mean by ‘Minimalist syntax’ ◮ Syntactic theories in the ST →EST →REST →GB →. . . ‘Chomskyan’ The form of syntactic theory assumed tradition, i.e. as opposed to LFG, HPSG etc. ◮ So nothing especially cutting-edge. But: Implementation of Glue in Minimalism ◮ The factoring together of subcategorization and structure building (in the mechanism of feature-checking) is, if not crucial to this analysis, Some features of the implementation then certainly useful.

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Rules of inference for the ⊸ fragment of intuitionistic propositional linear ◮ Often called a ‘logic of resources’ (Crouch and van Genabith, 2000, p. logic and their images under the Curry-Howard correspondence. 5). ⊸ elimination (linear modus ponens) corresponds to application ◮ Key difference from classical logic: for f A ⊸ B x A : : ⊸E premise 1,..., premise n ⊢ conclusion f (x) : B to be valid, each premise must be ‘used’ exactly once. So ⊸ ◮ A ⊢ A but A, A 0 A introduction (linear conditional proof) corresponds to abstraction ◮ We will only be concerned with a small fragment in this talk: [x : A]n . implication and the universal quantifier only connectives that will be . used. Φ : B n ⊸I λx.Φ : A ⊸ B

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax A fast introduction to Glue semantics A fast introduction to Glue semantics Linear logic and Glue Linear logic and Glue A simple example Quantifier

(1) John loves Mary.

John loves Mary (2) Someone loves everyone.

t  * someone loves everyone j′ B λy.λ x. ′ x, y A ⊸ B ⊸ C m′ A : love ( ) : ( ) : v  ( ′ λP.some ′(person ′, P) : λy.λ x.love (x, y) : λQ.every ′(person ′, Q) : ′ ⊸ ⊸ ′ λy.λ x.love (x, y) : A (B C) m : A (B ⊸ C) ⊸ C A ⊸ (B ⊸ C) (A ⊸ C) ⊸ C ′ ⊸E λx.love (x, m′) : B ⊸ C j′ : B ′ ⊸E love (j′, m′) : C

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′ λz.λ v.love (v, z) y 1 h i ′ : A ⊸ (B ⊸ C) : A λz.λ v.love (v, z) y 1 ′ ⊸E λv.love (v, y) x 2 : A ⊸ (B ⊸ C) h: Ai h: Bi ⊸ : B ⊸ C ⊸ ′ ′ ′ E ′ E λP.some (person , P) λv.love (v, y) love (x, y) : ( B ⊸ C) ⊸ C : B ⊸ C : C 1 ⊸ ′ ′ ′ ⊸I ′ ′ ′ E λQ.every (person , Q) λy.love (x, y) some (person , λ x.love (x, y)) ⊸ ⊸ ⊸ : ( A C) C : A C : C ⊸ 1 ′ ⊸E ′ ′ ′ ′ ′ I every ′(person ′, (λy.love (x, y))) λQ.every (person , Q) λy.some (person , λ x.love (x, y)) : C : ( A ⊸ C) ⊸ C : A ⊸ C ⊸I 2 ′ ′ ′ ′ ′ ′ ⊸E λP.some (person , P) λx.every (person , (λy.love (x, y))) every ′(person ′, λ y.some ′(person ′, λ x.love (x, y))) : C : ( B ⊸ C) ⊸ C : B ⊸ C ′ ⊸E some ′(person ′, λ x.every ′(person ′, λ y.love (x, y))) : C

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax A fast introduction to Glue semantics A fast introduction to Glue semantics The fragment to be used The fragment to be used LL λ calculus Meaning constructors implicational functional as types type f A ⊸ B x A : : ⊸E rules as ⊸ elimination application f (x) : B Following Kokkonidis (2008), I’ll use a fragment of (monadic) first-order operations [x : A]n linear logic as the glue language. . ⊸ introduction abstraction . ◮ Predicates: e and t Φ : B n ⊸I λ . ⊸ ◮ Constants: 1 , 2, 3 . . . x Φ : A B ◮ Φ : ∀X .A Variables: X , Y , Z . . . ∀ elimination — ∀E Φ : A[X ←c] ◮ Connectives: ⊸ and ∀ c free for X I’ll use subscript notation, e.g. e1 ⊸ tX instead of e(1) ⊸ t(X ). Φ : A ∀ introduction — ∀I Φ : ∀X .A X not free in any open leaf

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Basic ideas Features Largely based on Adger (2003) and Adger (2010)

◮ Syntactic objects have features. ◮ Some features describe what an LI is . ◮ The structure-building operation(s) (Merge) is/are based on the ◮ Some features describe what an LI needs (uninterpretable features). matching of features. Those can be strong(*) or weak. ◮ Every feature bears an index, and when two features match their V T indices must also match. huD, uDi h uD* i ◮ Those indices are used to label linear logic formulae paired with | | interpretations, thereby providing the syntax/semantics connection. love -s

(I’m going to ignore morphosyntactic features and agreement.)

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax The form of syntactic theory assumed The form of syntactic theory assumed

Structure-building operation(s) Hierarchy of projections

Adger (2003) has: Merge. Clausal: C i T i (Neg) i (Perf) i (Prog) i (Pass) i v i V ◮ Hierarchy of Projections-driven. Nominal: D i (Poss) i n i N ◮ Selectional features-driven. Adjectival: (Deg) i A ◮ External. ◮ Internal. We’ll use: Clausal: C i T i V Nominal: D i N

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HoPs merge Select merge External

A Where A and B are in the A . . . h. . . i same hierarchy of projections h i A + B ⇒ h. . . i (HoPs) and A is higher on that A huB,... i + B ⇒ A B HoPs than B A B huBi

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax The form of syntactic theory assumed The form of syntactic theory assumed

Select merge External merge Internal An example

A h. . . i V huDi A A V D huB* ,... i huB* i huD, uDi + ⇒ V D ⇒ huDi Mary love ... B ...... B ... love Mary

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External merge HoPs merge An example An example

T huD* i V V V huDi T V D V D V D huDi T huDi u + V D ⇒ h D* i -s D V huDi + ⇒ huDi John John V D John V D huDi -s huDi love Mary John V D huDi love Mary love Mary love Mary

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax The form of syntactic theory assumed Implementation of Glue in Minimalism

Internal merge Indices An example ′ ′ T1 λz.λ v.love (v, z) : e2 ⊸ (e3 ⊸ t1) m : e2 ⊸E T1 λ . ′ , ′ ⊸ ′ v love (v m ) : e3 t1 j : e3 ⊸ T ′ ′ ′ E huD* i T1 love (j , m ) : t1 T huD* i huD* 2i V1 T V λ .λ . ′ , T1 V1 huD2, uD3i z v love (v z) T V | : e2 ⊸ (e3 ⊸ t1) -s love D V ⇒ -s D V huDi -s 3 1 D V huD i D huDi 3 3 ′ △ j : e3 John V D John huDi John V1 D2 John V D huD2i huDi D2 ′ love Mary △ m : e2 love Mary Mary love Mary M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB2015 23/34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB2015 24/34 Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax Implementation of Glue in Minimalism Implementation of Glue in Minimalism

Surface scope interpretation T1 ′ ′ λP.every (person , P) : ∀X .(e3 ⊸ tX ) ⊸ tX E ′ ′ ∀ ′ T1 λP.every (person , P) : ( e3 ⊸ t1) ⊸ t1 λz.λ v.love (v, z) y 1 : e huD* 2i : e2 ⊸ (e3 ⊸ t1) h 2i ⊸E ′ ′ ′ 2 λP.some (person , P) : ∀X .(e2 ⊸ tX ) ⊸ tX λv.love (v, y) x E ⊸ h: e3i T1 V1 ′ ′ ∀ : e3 t1 ⊸ λP.some (person , P) : ( e ⊸ t ) ⊸ t ′ E 2 1 1 love (x, y) : t1 1 -s ′ ′ ′ ′ ′ ⊸I D3 V1 D3 λP.every (person , P) λQ.every (person , Q) λy.love (x, y) △ : ( e ⊸ t ) ⊸ t : e ⊸ t huD3i X . e ⊸ tX ⊸ tX 2 1 1 2 1 ⊸ everyone : ∀ ( 3 ) ′ ′ ′ E every (person , (λy.love (x, y))) everyone : t1 2 V1 D2 D ′ ′ ′ ′ ′ ′ ′ ⊸I 2 λP.some (person , P) λP.some (person , P) λx.every (person , (λy.love (x, y))) huD2i △ : ( e ⊸ t ) ⊸ t : e ⊸ t : ∀X .(e2 ⊸ tX ) ⊸ tX 3 1 1 3 1 ⊸ someone ′ ′ ′ ′ ′ E some (person , λ x.every (person , λ y.love (x, y))) : t1 love someone

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax Implementation of Glue in Minimalism Some features of the implementation

Inverse scope interpretation Embedded QPs

(3) No owner of an espresso machine drinks tea.

′ Analysis by (Heim and Kratzer, 1998, p. 229) of the surface scope reading: λz.λ v.love (v, z) y 1 : e DP : e2 ⊸ (e3 ⊸ t1) h 2i ′ ′ ′ ⊸E λP.some (person , P) λv.love (v, y) D NP ⊸ ⊸ ⊸ : ( e3 t1) t1 : e3 t1 ⊸ ′ ′ ′ E no some (person , λ x.love (x, y)) DP 1 NP : t1 1 pro ′ ′ ′ ⊸I DP NP λQ.every (person , Q) λy.some ′(person ′, λ x.love (x, y)) 2 ⊸ ⊸ ⊸ : ( e2 t1) t1 : e2 t1 ⊸ an espresso DP ′ ′ ′ ′ ′ E N every (person , λ y.some (person , λ x.love (x, y))) : t1 machine t1 N PP owner P DP

of t2

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′ 1 N1 ′ λz.λ v.own (v, z) y N1 λz.λ v. v, z ⊸ ⊸ h: e2i huP2i own ( ) : e2 (e1 t1) ′ ⊸E | : e2 ⊸ (e1 ⊸ t1) λv.own (v, y) x 2 ⊸ : e1 N PP owner : e1 t1 h i 1 2 ′ ⊸E huP i own (x, y) 2 3 P2 : t1 1 ′ ′ ′ ⊸I λw.w z huD3i λP.some (machine , P) λy.own (x, y) : e3 ⊸ e2 h: e3i owner λw.w : e3 ⊸ e2 ⊸E P2 D3 : ∀X .(e ⊸ tX ) ⊸ tX : e2 ⊸ t1 z : e2 | 3 ⊸E ′ ′ ∀E ′ huD3i λP.some (machine , P) own (x, z) : t1 of ⊸I 3 ⊸ ⊸ λ . ′ , ⊸ : ( e3 t1) t1 z own (x z) : e3 t1 ⊸ ′ ′ ′ ′ ′ E of an espresso D3 λP. , P some (machine , λ z.own (x, z)) : t1 some (machine ) ⊸ 2 machine △ ⊸ ⊸ ′ ′ ′ ⊸ I an e.m. : ∀X .(e3 tX ) tX λx.some (machine , λ z.own (x, z)) : e1 t1

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax Some features of the implementation Some features of the implementation

(Overt) movement Trace theory was abandoned in early minimalism in favor of the so-called copy theory of movement. Indices were deemed NP incompatible with the principle of Inclusiveness, which restricts the content of tree structures to information originating in the N CP lexicon. Because indices of phrases cannot be traced back to any woman DP C lexical entry, they are illegitimate syntactic objects. who(m) C TP (Neeleman and van de Koot, 2010, p. 331) D T If we assume that the computational system of syntax doesn’t use variables, variables are introduced at the point where the John T VP LF-structure of a sentence is translated into a semantic -s V DP representation.

love who(m) (Sauerland, 1998, p. 196)

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C1[rel]

C [rel] 1 C[rel] λP.λ Q.λ x.P(x) ∧ Q(x) : huwh* 3i 1 huwh* i (e ⊸ t ) ⊸ (( e ⊸ t ) ⊸ (e ⊸ t )) ′ 3 3 1 1 1 1 1 λz.λ v.love (v, z) C1[rel] T1 1 : e3 ⊸ (e2 ⊸ t1) [ y : e3] ′ ⊸E T1 λv.love (v, y) e ⊸ t j′ e huD* 2i : 2 1 : 2 ⊸ λP.λ Q.λ x.P(x) ∧ Q(x) ′ ′ E : ( e ⊸ t ) ⊸ love (j , y) : t1 T V 3 1 ⊸I 1 1 1 ⊸ ⊸ ⊸ λ . ′ ′, ⊸ (( e1 t1) (e1 t1)) y love (j y) : e3 t1 ⊸ ′ ′ E -s D2 V1 λQ.λ x.love (j , x) ∧ Q(x) : ( e1 ⊸ t1) ⊸ (e1 ⊸ t1) huD2i

John V1 D3[wh] huD3i

love who(m)

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Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax

References I II

Crouch, Richard and Josef van Genabith (2000). “Linear Logic for Linguists”. ESSLLI 2000 course notes. Archived 2006-10-19 in the Adger, David (2003). Core Syntax: A Minimalist Approach . Core Internet Archive at Linguistics. Oxford: Oxford University Press. http://web.archive.org/web/20061019004949/http: – (2010). “A Minimalist theory of feature structure”. In: Features: //www2.parc.com/istl/members/crouch/esslli00_notes.pdf . Perspectives on a Key Notion in Linguistics . Ed. by Anna Kibort and Dalrymple, Mary, ed. (1999). Semantics and Syntax in Lexical Functional Greville G. Corbett. Oxford: Oxford University Press, pp. 185–218. Grammar: The Resource Logic Approach . Cambridge, MA: MIT Press. Asudeh, Ash and Richard Crouch (2002). “Glue Semantics for HPSG”. In: Frank, Anette and Josef van Genabith (2001). “GlueTag: Linear Proceedings of the 8th International HPSG Conference . (Norwegian Logic-based Semantics for LTAG—and what it teaches us about LFG University of Science and Technology, Trondheim). Ed. by and LTAG”. In: Proceedings of the LFG01 Conference . (University of Frank van Eynde, Lars Hellan, and Dorothee Beermann. Stanford, CA: Hong Kong). Ed. by Miriam Butt and Tracy Holloway King. Stanford, CSLI Publications. CA: CSLI Publications. Girard, Jean-Yves (1987). “Linear Logic”. In: Theoretical Computer Science 50.1, pp. 1–101. issn : 0304-3975.

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References III

Heim, Irene and Angelika Kratzer (1998). Semantics in . Blackwell Textbooks in Linguistics 13. Oxford: Wiley-Blackwell. Kokkonidis, Miltiadis (2008). “First-Order Glue”. In: Journal of Logic, Language and Information 17.1, pp. 43–68. Neeleman, Ad and Hans van de Koot (2010). “A Local Encoding of Syntactic Dependencies and Its Consequences for the Theory of Movement”. In: Syntax 13.4, pp. 331–372. Sauerland, Uli (1998). “The Meaning of Chains”. PhD thesis. Massachusetts Institute of Technology.

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