Results 21 to 30 of about 2,544 (97)

The Hidden Structural Rules of the Discontinuous Lambek Calculus

, 2013
The sequent calculus sL for the Lambek calculus L (lambek 58) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper
A. Avron, G. Morrill, G. Morrill, G. Morrill   +3 more
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Cyclic Shift in the Lambek Calculus

CoRR, 2021
We enrich the Lambek calculus with the cyclic shift operation, which is expected to model the closure operator of formal languages with respect to cyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination. Secondly, we turn to categorial grammars based on this calculus and show that they can generate non-context-free languages ...
openaire   +2 more sources

Semi-Substructural Logics à la Lambek with Symmetry

Bulletin of the Section of Logic
This work studies the proof theory and ternary relational semantics of left (right) skew monoidal closed categories and skew monoidal bi-closed categories, both symmetric and non-symmetric, from the perspective of non-associative Lambek calculus ...
Cheng-Syuan Wan
doaj   +1 more source

Complexity of Nonassociative Lambek Calculus with Classical and Intuitionistic Logic

Bulletin of the Section of Logic
The Nonassociative Lambek Calculus (NL) represents a logic devoid of the structural rules of exchange, weakening, and contraction, and it does not presume the associativity of its connectives. Its finitary consequence relation is decidable in polynomial
Paweł Płaczek
doaj   +1 more source

Variable binding, symmetric monoidal closed theories, and bigraphs [PDF]

, 2009
This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects.
A. Barber, A. Hirschowitz, F. Pfenning, J. Despeyroux, J. Lambek, J. Rathke, L. Cardelli, M. Coccia, M. Fiore, M. Hofmann, M. Tanaka, M.J. Gabbay, P. Gianantonio Di, R. Bruni, S. Mac Lane, V. Sassone, Y. Lafont   +16 more
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Models for the Lambek calculus

Annals of Pure and Applied Logic, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

A Frobenius Algebraic Analysis for Parasitic Gaps [PDF]

, 2020
The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify
Moortgat, Michael, Sadrzadeh, Mehrnoosh, Wijnholds, Gijs   +2 more
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Comparing and evaluating extended Lambek calculi [PDF]

, 2015
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory ...
Moot, Richard
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Undecidability of the Lambek Calculus with a Relevant Modality [PDF]

, 2016
17 ...
Max I. Kanovich, Stepan L. Kuznetsov, Andre Scedrov   +2 more
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Sequent Systems for Consequence Relations of Cyclic Linear Logics

Bulletin of the Section of Logic
Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free component of the larger ...
Paweł Płaczek
doaj   +1 more source