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A normal modal calculus between T and S4 without the finite model property

Published online by Cambridge University Press:  12 March 2014

David Makinson*
Affiliation:
American University of Beirut, Beirut, Lebanon

Extract

Given separate though similar proofs of the finite model property for individual modal calculi such as S5, S4, S2, and the Feys-von Wright system T, the problem arises of generalising the arguments and establishing the property for modal calculi en masse. In other words, we would like to be able to show in one fell swoop that any modal calculus satisfying certain general syntactic conditions has the finite model property.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Bull, R. A., That all normal extensions of S4.3 have the finite model property, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 341344.CrossRefGoogle Scholar
[2]Harrop, R., Some structure results for prepositional calculi, this Journal, vol. 30 (1965), pp. 271292.Google Scholar
[3]Kripke, S. A., Semantical analysis of modal logic I. Normal modal propositional calculi, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 6196.CrossRefGoogle Scholar
[4]Lemmon, E. J., Algebraic semantics for modal logics I, this Journal, vol. 31 (1966), pp. 4665.Google Scholar
[5]Harrop, R., On the existence of finite models and decision procedures for propositional calculi, Proceedings of the Cambridge Philosophical Society, vol. 54 (1958), pp. 113.CrossRefGoogle Scholar