Journal of Philosophical Logic

, Volume 26, Issue 3, pp 241–250

T × W Completeness

  • Franz von Kutschera

DOI: 10.1023/A:1017942520078

Cite this article as:
Kutschera, F.v. Journal of Philosophical Logic (1997) 26: 241. doi:10.1023/A:1017942520078


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”.

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Franz von Kutschera
    • 1
  1. 1.Philosophische Fakultaet I, Lehrstuhl fuer PhilosophieUniversitaet RegenburgRegensburgGermany