Glue Semantics 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. ◮ Originally developed for LFG, and now the mainstream view of the Matthew Gotham 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 linear logic (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 categorial grammar) M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 1 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 2 / 34 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’ The form of syntactic theory assumed ◮ Syntactic theories in the ST → EST → REST → GB → . . . ‘Chomskyan’ tradition, i.e. as opposed to LFG, HPSG etc. Implementation of Glue in Minimalism ◮ So nothing especially cutting-edge. But: ◮ The factoring together of subcategorization and structure building (in Some features of the implementation the mechanism of feature-checking) is, if not crucial to this analysis, then certainly useful. M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 3 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 4 / 34
� � � � � � 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 Linear logic Interpretation as deduction (Girard, 1987) Linear implication and functional types Rules of inference for the ⊸ fragment of intuitionistic propositional linear logic and their images under the Curry-Howard correspondence. ◮ Often called a ‘logic of resources’ (Crouch and van Genabith, 2000, p. 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 ⊸ introduction (linear conditional proof) corresponds to abstraction ◮ A ⊢ A but A , A � A ◮ 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 λ x . Φ : A ⊸ B ⊸ I n M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 5 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 6 / 34 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 scope ambiguity (1) John loves Mary. (2) Someone loves everyone. John loves Mary someone loves everyone j ′ : B m ′ : A λ y .λ x . love ′ ( x , y ) : A ⊸ ( B ⊸ C ) λ y .λ x . love ′ ( x , y ) : λ P . some ′ (person ′ , P ) : λ Q . every ′ (person ′ , Q ) : m ′ : A λ y .λ x . love ′ ( x , y ) : A ⊸ ( B ⊸ C ) ( B ⊸ C ) ⊸ C A ⊸ ( B ⊸ C ) ( A ⊸ C ) ⊸ C ⊸ E j ′ : B λ x . love ′ ( x , m ′ ) : B ⊸ C ⊸ E love ′ ( j ′ , m ′ ) : C M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 7 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 8 / 34
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 Surface scope interpretation Inverse scope interpretation � y λ z .λ v . love ′ ( v , z ) � 1 � y : A : A ⊸ ( B ⊸ C ) λ z .λ v . love ′ ( v , z ) � 1 ⊸ E � x � 2 λ v . love ′ ( v , y ) : A : A ⊸ ( B ⊸ C ) : B ⊸ E : B ⊸ C λ P . some ′ (person ′ , P ) λ v . love ′ ( v , y ) ⊸ E love ′ ( x , y ) : ( B ⊸ C ) ⊸ C : B ⊸ C : C ⊸ I 1 ⊸ E some ′ (person ′ , λ x . love ′ ( x , y )) λ Q . every ′ (person ′ , Q ) λ y . love ′ ( x , y ) : ( A ⊸ C ) ⊸ C : A ⊸ C : C ⊸ I 1 ⊸ E λ Q . every ′ (person ′ , Q ) λ y . some ′ (person ′ , λ x . love ′ ( x , y )) every ′ (person ′ , ( λ y . love ′ ( x , y ))) : C : ( A ⊸ C ) ⊸ C : A ⊸ C ⊸ I 2 ⊸ E λ P . some ′ (person ′ , P ) λ x . every ′ (person ′ , ( λ y . 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 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 9 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 10 / 34 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 propositions implicational functional as types proposition type f : A ⊸ B x : A ⊸ E rules as ⊸ elimination application f ( x ) : B operations Following Kokkonidis (2008), I’ll use a fragment of (monadic) first-order [ x : A ] n linear logic as the glue language. . . . . ⊸ introduction abstraction ◮ Predicates: e and t Φ : B λ x . Φ : A ⊸ B ⊸ I n ◮ Constants: 1 , 2 , 3 . . . ◮ Variables: X , Y , Z . . . Φ : ∀ X . A ∀ elimination — Φ : A [ X ← c ] ∀ E ◮ Connectives: ⊸ and ∀ c free for X I’ll use subscript notation, e.g. e 1 ⊸ t X instead of e (1) ⊸ t ( X ). Φ : A ∀ introduction — Φ : ∀ X . A ∀ I X not free in any open leaf M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 11 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 12 / 34
Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax The form of syntactic theory assumed The form of syntactic theory assumed Basic ideas Features Largely based on Adger (2003) and Adger (2010) ◮ Some features describe what an LI is . ◮ Syntactic objects have features. ◮ Some features describe what an LI needs (uninterpretable features). ◮ The structure-building operation(s) (Merge) is/are based on the Those can be strong(*) or weak. matching of features. ◮ Every feature bears an index, and when two features match their V T indices must also match. � u D , u D � � u D* � ◮ 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.) M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 13 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 14 / 34 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: Clausal: C � T � (Neg) � (Perf) � (Prog) � (Pass) � v � V Merge. Nominal: D � (Poss) � n � N ◮ Hierarchy of Projections-driven. Adjectival: (Deg) � A ◮ Selectional features-driven. ◮ External. We’ll use: ◮ Internal. Clausal: C � T � V Nominal: D � N M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 15 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 16 / 34
Glue Semantics for Minimalist Syntax Glue Semantics for Minimalist Syntax The form of syntactic theory assumed The form of syntactic theory assumed HoPs merge Select merge External Where A and B are in the A A � . . . � � . . . � same hierarchy of projections A + B ⇒ A � . . . � (HoPs) and A is higher on that + B ⇒ � u B , . . . � A B HoPs than B A B � u B � M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 17 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 18 / 34 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 � . . . � V � u D � A V A D � u D , u D � � u B* � � u B* , . . . � + ⇒ V D ⇒ � u D � Mary love . . . B . . . . . . B . . . love Mary M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 19 / 34 M Gotham (UCL) Glue Semantics for Minimalist Syntax LAGB 2015 20 / 34
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