PP-2002-09: A Sahlqvist Theorem for Distributive Modal Logic

PP-2002-09: Gehrke, Mai and Nagahashi, Hideo and Venema, Yde (2002) A Sahlqvist Theorem for Distributive Modal Logic. [Report]

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Abstract

In this paper we consider distributive modal logic, a setting in which we may add modalities, such as classical types of modalities as well as weak forms of negation, to the fragment of classical propositional logic given by conjunction, disjunction, true, and false. For these logics we define both algebraic semantics, in the form of distributive modal algebras, and relational semantics, in the form of ordered Kripke structures. The main contributions of this paper lie in extending the notion of Sahlqvist axioms to our generalized setting and proving both a correspondence and a canonicity result for distributive modal logics axiomatized by Sahlqvist axioms. Our proof of the correspondence result relies on a reduction to the classical case, but our canonicity proof departs from the traditional style and uses the newly extended algebraic theory of canonical extensions.

Item Type: Report
Report Nr: PP-2002-09
Series Name: Prepublication (PP) Series
Year: 2002
Uncontrolled Keywords: distributive modal logic, distributive modal algebras, lattice expansions, canonical extensions, correspondence theory, canonical logic, canonical varieties, duality
Subjects: Logic
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/73

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