David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Journal of Symbolic Logic 58 (1):139-157 (1993)
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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Citations of this work BETA
Jan van Eijck & Fer-Jan de Vries (1995). Reasoning About Update Logic. Journal of Philosophical Logic 24 (1):19-45.
Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner (1999). On Finite Model Property for Admissible Rules. Mathematical Logic Quarterly 45 (4):505-520.
Nick Bezhanishvili (2008). Frame Based Formulas for Intermediate Logics. Studia Logica 90 (2):139-159.
Yutaka Miyazaki (2007). A Splitting Logic in NExt. Studia Logica 85 (3):381-394.
Guram Bezhanishvili & Nick Bezhanishvili (2012). Canonical Formulas for Wk4. Review of Symbolic Logic 5 (4):731-762.
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