T × W Completeness

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...

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Bibliographic Details
Published inJournal of philosophical logic Vol. 26; no. 3; pp. 241 - 250
Main Author Kutschera, Franz von
Format Journal Article
LanguageEnglish
Published Dordrecht Reidel Pub. Co 01.06.1997
Springer Nature B.V
Subjects
Causality
Logic
Temporal logic
Tense
Truth
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Summary: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".
ISSN:0022-3611
1573-0433
DOI:10.1023/A:1017942520078