Journal of Philosophical Logic 26 (3):241-250 (1997)

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”.
Keywords Philosophy
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DOI 10.1023/A:1017942520078
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Combinations of Tense and Modality for Predicate Logic.Stefan Wölfl - 1999 - Journal of Philosophical Logic 28 (4):371-398.
Propositional Q-Logic.Stefan Wölfl - 2002 - Journal of Philosophical Logic 31 (5):387-414.
Axiomatizing Hybrid Products.Katsuhiko Sano - 2010 - Journal of Applied Logic 8 (4):459-474.

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