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Involutive Commutative Residuated Lattice without Unit: Logics and Decidability
Abstract
We investigate involutive commutative residuated lattices without unit, which are commutative residuated lattice-ordered semigroups enriched with a unary involutive negation operator. The logic of this structure is discussed and the Genzten-style sequent calculus of it is presented. Moreover, we prove the decidability of this logic.Author Profiles
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References found in this work
Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Adding involution to residuated structures.Nikolaos Galatos & James G. Raftery - 2004 - Studia Logica 77 (2):181 - 207.
The Lambek calculus enriched with additional connectives.Makoto Kanazawa - 1992 - Journal of Logic, Language and Information 1 (2):141-171.
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