Models for polymorphic Lambek Calculus

Emms, Martin

doi:10.1007/bfb0052157

Cited by 3 publications

(4 citation statements)

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“…Finally, given that the Lambek calculus with assignments to the empty string is known to be undecidable [2], adding assignments to the empty string to HTLG results in an undecidable system as well. Similarly, since the Lambek calculus with second-order quantifiers is known to be undecidable [7], the same holds for HTLG. We leave open the question of whether the methods for making secondorder quantifiers decidable in the categorial grammar and linear logic tradition [6,22,32] can be adapted to type-logical grammar.…”

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confidence: 78%

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Logical foundations for hybrid type-logical grammars

Moot¹,

Stevens-Guille²

2020

Preprint

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This paper explores proof-theoretic aspects of hybrid type-logical grammars, a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also present both a sequent and a proof net calculus for hybrid type-logical grammars. In addition to clarifying the logical foundations of hybrid type-logical grammars, the current study opens the way to variants and extensions of the original system, including but not limited to a non-associative version and a multimodal version incorporating structural rules and unary modes.This is a significantly extended version of a paper presented at Formal Grammar 2019 [28]. We thank the referees of Formal Grammar as well as the audience of the conference for their invaluable feedback.

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confidence: 78%

“…Proof nets are a graph theoretic representation of proofs introduced for linear logic by Girard [8]. Proof nets remove the possibility of 'boring' rule permutations as they occur in the sequent calculus or natural deduction, 7 solving the so-called problem of 'spurious ambiguity' in type-logical grammars.…”

Section: Proof Netsmentioning

confidence: 99%

Logical foundations for hybrid type-logical grammars

Moot¹,

Stevens-Guille²

2020

Preprint

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“…Papers by: Došen; Belnap; Bunder; Dunn; Gabbay; Kron; Lambek; Meyer and Mares; Ono; Sambin; Soloviev; Troelstra; and van Benthem. 19 But in general there is undecidability: Emms (1995). 20 In both cases the prosodic algebras contain (infinitely many) terms in which ordered pairing or juxtaposition is embedded, therefore inaccessible to any eventual wrapping, therefore junk.…”

Section: Schroeder-heister and Došen (1993)mentioning

confidence: 97%

A Chronicle of Type Logical Grammar: 1935–1994

Morrill

2007

Res on Lang and Comput

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Categorial grammar predated Syntactic Structures by two decades. While dramatic linguistic revolutions occupied centre stage, it tended to be the preserve of formal philosophy and philosophical linguistics: the philosophers' grammar. Fashions change but style endures. The 1980s saw the rediscovery of the categorial calculus of Lambek (1958) and the advent of linear logic and substructural logic generally providing a context for categorial grammar so-construed, since named type logical grammar (TLG). I think the history of the genesis and evolution of type-logical ideas is not widely known, but that the interpretation of the past is important to give direction to the future. This is the story of how a field came to a new pass.The point of departure for categorial grammar can be seen as Frege's position that there are certain 'complete expressions' which are the primary bearers of meaning, and that the meanings of 'incomplete expressions' (including words) are derivative, being their contribution to the meanings of the expressions in which they occur.Work partially funded by the DGICYT project TIN2005-08832-C03-03 (MOISES-BAR). I thank a RoLC reviewer for most useful comments and suggestions, and Mario Fadda, Oriol Valentín and David Weir. This account reports my experience and interests; the opinions are mine and all errors are my own.

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“…This is done by using polymorphic types, predicatively universally quantifying over category variables. A treatment of extraction by means of polymorphic Lambek calculus can be found in [3].…”

Section: Introductionmentioning

confidence: 99%