Duality and canonical extensions of bounded distributive lattices with operators, and applications to the semantics of non-classical logics II
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 64 (2):151-172 (2000)
The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Ivo Düntsch & Ewa Orłowska (2004). Boolean Algebras Arising From Information Systems. Annals of Pure and Applied Logic 127 (1-3):77-98.
Similar books and articles
J. Michael Dunn, Mai Gehrke & Alessandra Palmigiano (2005). Canonical Extensions and Relational Completeness of Some Substructural Logics. Journal of Symbolic Logic 70 (3):713 - 740.
B. Konev, R. Kontchakov, F. Wolter & M. Zakharyaschev (2006). On Dynamic Topological and Metric Logics. Studia Logica 84 (1):129 - 160.
Dominic Gregory (2001). Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators. Journal of Philosophical Logic 30 (1):57-78.
Claudia B. Wegener (2002). Free Modal Lattices Via Priestley Duality. Studia Logica 70 (3):339 - 352.
David Basin, Seán Matthews & Luca Viganò (1998). Natural Deduction for Non-Classical Logics. Studia Logica 60 (1):119-160.
Josep M. Font & Ventura Verdú (1993). The Lattice of Distributive Closure Operators Over an Algebra. Studia Logica 52 (1):1 - 13.
Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
Ross T. Brady (1989). A Content Semantics for Quantified Relevant Logics. II. Studia Logica 48 (2):243 - 257.
Alasdair Urquhart (1996). Duality for Algebras of Relevant Logics. Studia Logica 56 (1-2):263 - 276.
Added to index2009-01-28
Total downloads9 ( #177,826 of 1,410,159 )
Recent downloads (6 months)1 ( #177,870 of 1,410,159 )
How can I increase my downloads?