The Logic of World States
We have already had occasion to consider whether certain conditions on the U-relation are or are not expressible in terms of tense operators alone. For example, we have seen in the context of the completeness proof for K t , that irreflexivity of U is not so expressible1. We shall now present some further results along these lines, using a calculus of “world states” which gives some hope that the R-calculi can be developed within pure tense calculi.
KeywordsModal Logic Temporal Logic Completeness Proof World State Complete History
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- 2.For a presentation of Meredith’s findings, see A. N. Prior, Past, Present and Future (Oxford, 1967 ), pp. 77–79.Google Scholar
- 3.Compare the opening sentences of L. Wittgenstein’s Tractatus Logico Philosophicus (London, 1922).Google Scholar
- 5.For details, see Prior, op. cit., pp. 88–92, 187–197, and Paper XI in: Prior, Papers on Time and Tense (Oxford, 1968 ).Google Scholar