Splittings and the finite model property

Journal of Symbolic Logic 58 (1):139-157 (1993)

Abstract

An old conjecture of modal logics states that every splitting of the major systems K4, S4, G and Grz has the finite model property. In this paper we will prove that all iterated splittings of G have fmp, whereas in the other cases we will give explicit counterexamples. We also introduce a proof technique which will give a positive answer for large classes of splitting frames. The proof works by establishing a rather strong property of these splitting frames namely that they preserve the finite model property in the following sense. Whenever an extension Λ has fmp so does the splitting Λ/f of Λ by f. Although we will also see that this method has its limitations because there are frames lacking this property, it has several desirable side effects. For example, properties such as compactness, decidability and others can be shown to be preserved in a similar way and effective bounds for the size of models can be given. Moreover, all methods and proofs are constructive

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References found in this work

An Incomplete Logic Containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
An Ascending Chain of S4 Logics.Kit Fine - 1974 - Theoria 40 (2):110-116.
Modal Tableau Calculi and Interpolation.Wolfgang Rautenberg - 1983 - Journal of Philosophical Logic 12 (4):403 - 423.
Splitting Lattices of Logics.Wolfgang Rautenberg - 1980 - Archive for Mathematical Logic 20 (3-4):155-159.

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Citations of this work

Canonical Formulas for Wk4.Guram Bezhanishvili & Nick Bezhanishvili - 2012 - Review of Symbolic Logic 5 (4):731-762.
Reasoning About Update Logic.Jan van Eijck & Fer-Jan de Vries - 1995 - Journal of Philosophical Logic 24 (1):19-45.
A Splitting Logic in NExt(KTB).Yutaka Miyazaki - 2007 - Studia Logica 85 (3):381 - 394.

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