Canonical Extensions and Relational Completeness of Some Substructural Logics

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Journal of Symbolic Logic 70 (3):713 - 740 (2005)
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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

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10.2178/jsl/1122038911

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James Dunn
University of Edinburgh

Citations of this work

Generalized Kripke Frames.Mai Gehrke - 2006 - Studia Logica 84 (2):241-275.
Order algebraizable logics.James G. Raftery - 2013 - Annals of Pure and Applied Logic 164 (3):251-283.
B-frame duality.Guillaume Massas - 2023 - Annals of Pure and Applied Logic 174 (5):103245.

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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.

View all 8 references / Add more references