Open Access
2011 An Algebraic Approach to Subframe Logics. Modal Case
Guram Bezhanishvili, Silvio Ghilardi, Mamuka Jibladze
Notre Dame J. Formal Logic 52(2): 187-202 (2011). DOI: 10.1215/00294527-1306190


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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Guram Bezhanishvili. Silvio Ghilardi. Mamuka Jibladze. "An Algebraic Approach to Subframe Logics. Modal Case." Notre Dame J. Formal Logic 52 (2) 187 - 202, 2011.


Published: 2011
First available in Project Euclid: 28 April 2011

zbMATH: 1246.03041
MathSciNet: MR2794651
Digital Object Identifier: 10.1215/00294527-1306190

Primary: 03B45

Keywords: finite model property , modal logic , subframe logic

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 2 • 2011
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