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Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity
Bulletin of the Section of Logic 46 (1/2) (2017)
Abstract
In [5] we study Nonassociative Lambek Calculus augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus. Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.Links
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Citations of this work
One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity.Paweł Płaczek - 2021 - Bulletin of the Section of Logic 50 (1):55-80.
Sequent systems for consequence relations of cyclic linear logics.Paweł Płaczek - forthcoming - Bulletin of the Section of Logic:30 pp..
A Substructural Gentzen Calculus for Orthomodular Quantum Logic.Davide Fazio, Antonio Ledda, Francesco Paoli & Gavin St John - 2023 - Review of Symbolic Logic 16 (4):1177-1198.
On Involutive Nonassociative Lambek Calculus.Wojciech Buszkowski - 2019 - Journal of Logic, Language and Information 28 (2):157-181.
References found in this work
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic.V. Michele Abrusci - 1991 - Journal of Symbolic Logic 56 (4):1403-1451.
The finite model property for various fragments of intuitionistic linear logic.Mitsuhiro Okada & Kazushige Terui - 1999 - Journal of Symbolic Logic 64 (2):790-802.
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