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Canonical extensions and relational completeness of some substructural logics
Journal of Symbolic Logic 70 (3):713-740 (2005)
Abstract
In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.Author's Profile
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Citations of this work
Algorithmic correspondence and canonicity for distributive modal logic.Willem Conradie & Alessandra Palmigiano - 2012 - Annals of Pure and Applied Logic 163 (3):338-376.
Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
Generalising canonical extension to the categorical setting.Dion Coumans - 2012 - Annals of Pure and Applied Logic 163 (12):1940-1961.
Modal translation of substructural logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.
References found in this work
Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.
A Sahlqvist theorem for distributive modal logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1-3):65-102.
Constructive canonicity in non-classical logics.Silvio Ghilardi & Giancarlo Meloni - 1997 - Annals of Pure and Applied Logic 86 (1):1-32.
Kripke semantics for modal substructural logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
A Kripke semantics for the logic of Gelfand quantales.Gerard Allwein & Wendy MacCaull - 2001 - Studia Logica 68 (2):173-228.
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