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Semantics for RKt1

Published online by Cambridge University Press:  12 March 2014

M. K. Rennie
M. K. Rennie*
Affiliation:
University of Queensland, Brisbane, Australia
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Extract

In Chapter XIII of [4], Prior discusses a system QKt, designed to stand to the “minimal” tense logic Kt as the modal system Q of [3] stands to S5. In this paper I provide semantics for a similar system, slightly weaker than QKt: the weakening is due to the fact that Prior's axioms are slightly too strong for a “minimal” system. An extended post-Henkin style completeness proof for the axiomatization with respect to the semantics provided is then given: the underlying three-valued nature of the semantics requires a twist in the proof which is new to its author at least, and also results in some details being set out which could well be glossed over in the two-valued case.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 1 , March 1971 , pp. 97 - 107
Copyright
Copyright © Association for Symbolic Logic 1971

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Footnotes

1

For the detection of an error in the original, I want to thank Robert Bull: its correction is due to Dov Gabbay.

References

[1]Hughes, G. E. and Cresswell, M. J., An introduction to modal logic, Methuen, London, 1968.Google Scholar
[2]Makinson, D. C., On some completeness theorems in modal logic, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 379–384.CrossRefGoogle Scholar
[3]Prior, A. N., Time and modality, Clarendon Press, Oxford, 1957.Google Scholar
[4]Prior, A. N., Papers on time and tense, Clarendon Press, Oxford, 1968.Google Scholar
[5]Rennie, M. K., On postulates for temporal order, The Monist, vol. 3 (1969), pp. 457–468.CrossRefGoogle Scholar