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An algebraic study of tense logics with linear time

Published online by Cambridge University Press:  12 March 2014

R. A. Bull
R. A. Bull*
Affiliation:
University of Birmingham
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Extract

In [2] Prior puts forward a tense logic, GH1, which is intended to axiomatise tense logic with time linear and rational; he also contemplates the tense logic with time linear and real. The purpose of this paper is to give completeness proofs for three axiom systems, GH1, GHlr, GHli, with respect to tense logic with time linear and rational, real, and integral, respectively.1 In a fourth section I show that GH1 and GHlr have the finite model property, but that GHli lacks it.

GH1 has the operators of the classical propositional calculus, together with operators P, H, F, G for ‘It has been the case that’, ‘It has always been the case that’, ‘It will be the case that’, ‘It will always be the case that’, respectively.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 27 - 38
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Bull, R. A., An algebraic study of Diodorean modal systems, this Journal, vol. 30 (1965), pp. 58–64.Google Scholar
[2]Prior, A. N., Postulates for tense-logic, American philosophical quarterly, vol. 3 (1966), no. 2, pp. 1–9.Google Scholar