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Tense logic for discrete future time

Published online by Cambridge University Press:  12 March 2014

Patrick Schindler
Patrick Schindler*
Affiliation:
Balliol College, Oxford
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Extract

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbol G, the definitions

Df. F: Fα = NGNα

Df. L: Lα = KαGα,

and the postulates

is complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:

Gli can be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 1 , March 1970 , pp. 105 - 118
Copyright
Copyright © Association for Symbolic Logic 1970

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References

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