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Completeness and Decidability of Tense Logics Closely Related to Logics Above K4

Frank Wolter
The Journal of Symbolic Logic
Vol. 62, No. 1 (Mar., 1997), pp. 131-158
DOI: 10.2307/2275736
Stable URL: http://www.jstor.org/stable/2275736
Page Count: 28
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Completeness and Decidability of Tense Logics Closely Related to Logics Above K4
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Abstract

Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are also presented.

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