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T × W Completeness

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Abstract

T × W logic is a combination of tense and modal logic for worlds or histories with the same time order. It is the basis for logics of causation, agency and conditionals, and therefore an important tool for philosophical logic. Semantically it has been defined, among others, by R. H. Thomason. Using an operator expressing truth in all worlds, first discussed by C. M. Di Maio and A. Zanardo, an axiomatization is given and its completeness proved via D. Gabbay’s irreflexivity lemma. Given this lemma the proof is more or less straight forward. At the end an alternative axiomatization is sketched in which Di Maio’s and Zanardo’s operator is replaced by a version of “actually”.

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  1. Philosophische Fakultaet I, Lehrstuhl fuer Philosophie, Universitaet Regenburg, D-93040, Regensburg, Germany

    Franz von Kutschera

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  1. Franz von Kutschera
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Kutschera, F.v. T × W Completeness. Journal of Philosophical Logic 26, 241–250 (1997). https://doi.org/10.1023/A:1017942520078

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  • DOI: https://doi.org/10.1023/A:1017942520078

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