Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T03:04:51.951Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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