Quantitative Logic and Soft Computing 2010 pp 311-319 | Cite as
Finite Topological Models of Modal Logic Systems S4 and S5
Conference paper
Abstract
In modal logic systems S4 and S5, some semantics equivalent theorems on various classes of models are proved. Main results are: (1) A formula is S4 (S5)-theorem if and only if it is globally true in any finite models of S4 (S5); (2) A formula is S4-theorem if and only if it is globally true in all finite topological models; (3) As a corollary of (2), Question 9.1.66 in [4] is affirmatively answered; (4) A formula is S5-theorem if and only if it is globally true in the class FCOT of finite topological models with open sets being closed.
Keywords
Modal logic model topological model filtration globally truePreview
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