An Algebraic Approach to Subframe Logics. Modal Case

Notre Dame Journal of Formal Logic 52 (2):187-202 (2011)
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Abstract

We prove that if a modal formula is refuted on a wK4-algebra ( B ,□), then it is refuted on a finite wK4-algebra which is isomorphic to a subalgebra of a relativization of ( B ,□). As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4 . On the other hand, it extends the Fine-Zakharyaschev results to wK4

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References found in this work

The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Logics containing k4. part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.
Logics containing k4. part II.Kit Fine - 1985 - Journal of Symbolic Logic 50 (3):619-651.
Topology and duality in modal logic.Giovanni Sambin & Virginia Vaccaro - 1988 - Annals of Pure and Applied Logic 37 (3):249-296.

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