Connected modal logics

Archive for Mathematical Logic 50 (3-4):287-317 (2011)
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Abstract

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.

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References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
« Everywhere » and « here ».Valentin Shehtman - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):369-379.

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