Type-Logical Grammar and Natural Language Syntax Yusuke Kubota - PowerPoint PPT Presentation

Type-Logical Grammar and Natural Language Syntax Yusuke Kubota University of Tsukuba kubota.yusuke.fn@u.tsukuba.ac.jp LACompLing 2018 Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 1 /44

Outline Overview of Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] ◮ A version of Type-Logical Grammar jointly developed with Bob Levine (OSU) Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 2 /44

Outline Overview of Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] ◮ A version of Type-Logical Grammar jointly developed with Bob Levine (OSU) Outline of presentation ◮ Motivations ◮ Basic architecture ◮ Linguistic application – Gapping in English Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 2 /44

Outline Overview of Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] ◮ A version of Type-Logical Grammar jointly developed with Bob Levine (OSU) Outline of presentation ◮ Motivations ◮ Basic architecture ◮ Linguistic application – Gapping in English ◮ Larger issues, open questions ◮ Comparison with some recent HPSG work ◮ Formal properties of Hybrid TLG ◮ Parsing Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 2 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Motivations: ◮ Logic-based version of CG ◮ (Relatively) easy to use for linguists ◮ Wide empirical coverage Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 3 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Motivations: ◮ Logic-based version of CG ◮ (Relatively) easy to use for linguists ◮ Wide empirical coverage Hybrid TLG builds on two lines of research in Type-Logical Grammar: ◮ Lambek calculus [Lambek, 1958] and its extensions ‘Syntax can be done (mostly) with order-sensitive implication’ Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 3 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Motivations: ◮ Logic-based version of CG ◮ (Relatively) easy to use for linguists ◮ Wide empirical coverage Hybrid TLG builds on two lines of research in Type-Logical Grammar: ◮ Lambek calculus [Lambek, 1958] and its extensions ‘Syntax can be done (mostly) with order-sensitive implication’ ◮ λ grammars [Oehrle, 1994, de Groote, 2001, Muskens, 2003, Mihaliˇ cek and Pollard, 2012] (see also [Ranta, 2004]) ‘Get rid of word order from syntax’ Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 3 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Motivations: ◮ Logic-based version of CG ◮ (Relatively) easy to use for linguists ◮ Wide empirical coverage Hybrid TLG builds on two lines of research in Type-Logical Grammar: ◮ Lambek calculus [Lambek, 1958] and its extensions ‘Syntax can be done (mostly) with order-sensitive implication’ ◮ λ grammars [Oehrle, 1994, de Groote, 2001, Muskens, 2003, Mihaliˇ cek and Pollard, 2012] (see also [Ranta, 2004]) ‘Get rid of word order from syntax’ local combinatorics non-local dependencies (e.g. coordination) (e.g. extraction, scope) Lambek calculus � * λ grammars * � Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 3 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Motivations: ◮ Logic-based version of CG ◮ (Relatively) easy to use for linguists ◮ Wide empirical coverage Hybrid TLG builds on two lines of research in Type-Logical Grammar: ◮ Lambek calculus [Lambek, 1958] and its extensions ‘Syntax can be done (mostly) with order-sensitive implication’ ◮ λ grammars [Oehrle, 1994, de Groote, 2001, Muskens, 2003, Mihaliˇ cek and Pollard, 2012] (see also [Ranta, 2004]) ‘Get rid of word order from syntax’ local combinatorics non-local dependencies (e.g. coordination) (e.g. extraction, scope) Lambek calculus � * λ grammars * � ◮ Hybrid TLG ≈ Lambek calculus + λ grammar Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 3 /44

Hybrid Type-Logical Grammar [Kubota, 2010, Kubota and Levine, 2015] Empirical results: ◮ coordination ◮ nonconstituent coordination [Kubota and Levine, 2015] ◮ Gapping [Kubota and Levine, 2016a] ◮ scopal operators ( same / different , respectively ) [Kubota and Levine, 2016b] ◮ ellipsis ◮ pseudogapping [Kubota and Levine, 2017] ◮ stripping [Puthawala, 2018] ◮ comparatives [Vaikˇ snorait˙ e, 2018] Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 4 /44

Lambek calculus Syntactic types ◮ A := { N, NP, S, . . . } (atomic type) ◮ T := A | T \T | T / T (type) Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 5 /44

Lambek calculus Syntactic types ◮ A := { N, NP, S, . . . } (atomic type) ◮ T := A | T \T | T / T (type) Syntactic rules of the Lambek calculus Forward Slash Elimination Backward Slash Elimination A / B B B B \ A / E \ E A A Forward Slash Introduction Backward Slash Introduction . . . . [ A ] n [ A ] n . . . . . . . . . . . . . . B B /I n \ I n B / A A \ B Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 5 /44

Sample derivation (1) (NP \ S)/NP [NP] 1 / E NP NP \ S ((S/NP) \ S)/N N S / I 1 S/NP (S/NP) \ S S NP (NP \ S)/NP ((S/NP) \ S)/N N ⊢ S John saw every student Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 6 /44

Derivation with prosodic term labelling (cf. [Morrill, 1994]) (2) � ϕ ; saw ; � 1 saw ; x ; ( NP \ S ) / NP NP john ; saw • ϕ ; every ; student ; j ; NP saw ( x ); NP \ S A ; student ; john • saw • ϕ ; (( S / NP ) \ S ) / N N saw ( x )( j ); S every • student ; / I 1 A john • saw ; student ; λx. saw ( x )( j ); S / NP ( S / NP ) \ S john • saw • every • student ; A student ( λx. saw ( x )( j )); S Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 7 /44

Lambek calculus, with semantic and prosodic term-labelling Forward Slash Introduction Forward Slash Elimination . . . [ ϕ ; x ; A ] n . . . a ; F ; A / B b ; G ; B . . . / E . . . . . . a • b ; F ( G ) ; A b • ϕ ; F ; B /I n b ; λx. F ; B / A Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 8 /44

Lambek calculus, with semantic and prosodic term-labelling Forward Slash Introduction Forward Slash Elimination . . . [ ϕ ; x ; A ] n . . . a ; F ; A / B b ; G ; B . . . / E . . . . . . a • b ; F ( G ) ; A b • ϕ ; F ; B /I n b ; λx. F ; B / A Backward Slash Introduction Backward Slash Elimination . . . . [ ϕ ; x ; A ] n . . b ; G ; B a ; F ; B \ A . . . . . . \ E . . . b • a ; F ( G ) ; A ϕ • b ; F ; B \ I n b ; λx. F ; A \ B Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 8 /44

Lambek calculus, with semantic and prosodic term-labelling Forward Slash Introduction Forward Slash Elimination . . . [ ϕ ; x ; A ] n . . . a ; F ; A / B b ; G ; B . . . / E . . . . . . a • b ; F ( G ) ; A b • ϕ ; F ; B /I n b ; λx. F ; B / A Backward Slash Introduction Backward Slash Elimination . . . . [ ϕ ; x ; A ] n . . b ; G ; B a ; F ; B \ A . . . . . . \ E . . . b • a ; F ( G ) ; A ϕ • b ; F ; B \ I n b ; λx. F ; A \ B ◮ Labelled deduction for notating the prosody (cf. [Morrill, 1994, Oehrle, 1994]). � Note: the prosodic terms are not proof terms in this setup. Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 8 /44

Lambek calculus Forward Slash Introduction Forward Slash Elimination . . . . [ ϕ ; x ; A ] n . . a ; F ; A / B b ; G ; B . . . / E . . . a • b ; F ( G ) ; A . . . b • ϕ ; F ; B /I n b ; λx. F ; B / A Backward Slash Introduction Backward Slash Elimination . . . . [ ϕ ; x ; A ] n . . b ; G ; B a ; F ; B \ A . . . \ E . . . b • a ; F ( G ) ; A . . . ϕ • b ; F ; B \ I n b ; λx. F ; A \ B Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 9 /44

Lambek calculus Forward Slash Introduction Forward Slash Elimination . . . . [ ϕ ; x ; A ] n . . a ; F ; A / B b ; G ; B . . . / E . . . a • b ; F ( G ) ; A . . . b • ϕ ; F ; B /I n b ; λx. F ; B / A Backward Slash Introduction Backward Slash Elimination . . . . [ ϕ ; x ; A ] n . . b ; G ; B a ; F ; B \ A . . . \ E . . . b • a ; F ( G ) ; A . . . ϕ • b ; F ; B \ I n b ; λx. F ; A \ B But. . . Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 9 /44

Lambek calculus Forward Slash Introduction Forward Slash Elimination . . . . [ ϕ ; x ; A ] n . . a ; F ; A / B b ; G ; B . . . / E . . . a • b ; F ( G ) ; A . . . b • ϕ ; F ; B /I n b ; λx. F ; B / A Backward Slash Introduction Backward Slash Elimination . . . . [ ϕ ; x ; A ] n . . b ; G ; B a ; F ; B \ A . . . \ E . . . b • a ; F ( G ) ; A . . . ϕ • b ; F ; B \ I n b ; λx. F ; A \ B But. . . What about syntactic movement? (3) a. I don’t know who i [John met i at the party]. b. John met every student yesterday. Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 9 /44

Syntactic movement in the Lambek calculus? (4) S everyone S λy S NP VP John VP PP V NP yesterday met y Yusuke Kubota Type-Logical Grammar and Natural Language Syntax 10 /44