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Weak liberated versions of T and S41

Published online by Cambridge University Press:  12 March 2014

Charles G. Morgan
Charles G. Morgan*
Affiliation:
University of Alberta, Edmonton, Canada
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Abstract

The usual semantics for the modal systems T, S4, and S5 assumes that the set of possible worlds contains at least one member. Recently versions of these modal systems have been developed in which this assumption is dropped. The systems discussed here are obtained by slightly weakening the liberated versions of T and S4. The semantics does not assume the existence of possible worlds, and the accessibility relation between worlds is only required to be quasi-reflexive instead of reflexive. Completeness and independence results are established.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 40 , Issue 1 , March 1975 , pp. 25 - 30
Copyright
Copyright © Association for Symbolic Logic 1975

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Footnotes

1

This research was supported by a grant from the Killam Foundation, administered by the Canada Council.

References

REFERENCES

[1]Hughes, G. E. and Cresswell, M. J., An introduction to modal logic, Methuen, London, 1968.Google Scholar
[2]Lambert, K., Leblanc, H. and Meyer, R., A liberated version of S5, Archiv für mathematische Logik und Grundlagenforschung, vol. 12 (1969), pp. 151–154.CrossRefGoogle Scholar
[3]Morgan, C. G., Liberated versions of T, S4, and S5, Archiv für mathematische Logik und Grundlagenforschung (forthcoming).Google Scholar
[4]Morgan, C. G., Liberated Brouwerian modal logic, Dialogue (forthcoming).Google Scholar