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Note on a system of Åqvist

Published online by Cambridge University Press:  12 March 2014

M. J. Cresswell
M. J. Cresswell*
Affiliation:
Victoria University of Wellington
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Extract

In [1, pp. 82–84] L. Åqvist considers a modal system which he calls S3.5 obtained by adding to S3 the axiom ∼□p⊃□∼□p. This system becomes S5 when the rule ├A→├□A is added to it. S3.5 is put forward to stand to S5 as S3 stands to S4 and S2 to T. In this note we show how a natural extension of the modelling for S3 in [2] can give a suitable semantics for S3.5.1

An S3 model2 is an ordered quadruple (GKRφ) where Κ is a set, G ε K and R is transitive and quasi-reflexive over K.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 58 - 60
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Åqvist, Lennart, Results concerning some modal systems that contain S2, this Journal vol. 29 (1964), pp. 79–87.Google Scholar
[2]Kripke, Saul A., Semantical analysis of modal logic. II. Non-normal modal prepositional calculi, The theory of models, Proceedings of the 1963 International Symposium at Berkeley, North Holland, Amsterdam, 1965, pp. 206–220.Google Scholar
[3]Kripke, Saul A., Semantical analysis of modal logic. I. Normal modal prepositional calculi, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 67–96.CrossRefGoogle Scholar
[4]Simons, Leo, New axiomatizations of S3 and S4, this Journal, vol. 18 (1953), pp. 309–316.Google Scholar