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Classical non-associative Lambek calculus
Studia Logica 71 (3):355-388 (2002)
Abstract
We introduce non-associative linear logic, which may be seen as the classical version of the non-associative Lambek calculus. We define its sequent calculus, its theory of proof-nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.My notes
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Citations of this work
A logic of non-monotonic interactions.Giovanni Boniolo, Marcello DʼAgostino, Mario Piazza & Gabriele Pulcini - 2013 - Journal of Applied Logic 11 (1):52-62.
Generalized Kripke semantics for the Lambek-Grishin calculus.A. Chernilovskaya, M. Gehrke & L. van Rooijen - 2012 - Logic Journal of the IGPL 20 (6):1110-1132.
Symmetric Categorial Grammar.Michael Moortgat - 2009 - Journal of Philosophical Logic 38 (6):681-710.
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.
Proof nets for the multimodal Lambek calculus.Richard Moot & Quintijn Puite - 2002 - Studia Logica 71 (3):415-442.
References found in this work
Categorial Type Logics.Michael Moortgat - 1997 - In J. van Benthem & A. ter Meulen (eds.), Handbook of Logic and Language. Elsevier.
Proof nets for the multimodal Lambek calculus.Richard Moot & Quintijn Puite - 2002 - Studia Logica 71 (3):415-442.
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