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Finite models constructed from canonical formulas. (English) Zbl 1132.03007
Summary: This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with K. Fine [Notre Dame J. Formal Logic 16, 229–237 (1975; Zbl 0245.02025)]. There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation D. Kozen and R. Parikh used in their proof of the completeness of PDL [Theor. Comput. Sci. 14, 113–118 (1981; Zbl 0451.03006)]. The point is to develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection.

03B45 Modal logic (including the logic of norms)
03B25 Decidability of theories and sets of sentences
03C13 Model theory of finite structures
Full Text: DOI
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