Completeness theorems via the double dual functor

Studia Logica 64 (1):61-81 (2000)
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Abstract

The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular, we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods.

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Citations of this work

Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Bi-Heyting algebras, toposes and modalities.Gonzalo E. Reyes & Houman Zolfaghari - 1996 - Journal of Philosophical Logic 25 (1):25 - 43.
Lukasiewicz and Symmetrical Heyting Algebras.Luisa Iturrioz - 1976 - Mathematical Logic Quarterly 23 (7‐12):131-136.
Moisil Algebras.Roberto Cignoli - 1975 - Journal of Symbolic Logic 40 (3):464-465.

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