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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REFERENCES
Burgess, J. P.: Basic tense logic, in: Gabbay and Guenthner (1984), 89–133.
Di Maio, M. C. and Zanardo, A.: Synchronized histories in Prior-Thomason representation of branching time, in: D. M. Gabbay and H. J. Ohlbach (eds): Temporal Logic (Proceedings of the First International Conference, ICTL ’94) Springer, Bonn, Berlin, 1994.
Gabbay, D. and Guenthner, F. (eds): Handbook of Philosophical Logic, vol. II, Kluwer, Dordrecht, 1984.
Gabbay, D.: An irreflexivity lemma with applications ot axiomatizations of conditions on tense frames, in: U. Mönnich (ed.), Aspects of Philosophical Logic, Reidel, Dordrecht, 1981, 67–89.
Gabbay, D., Hodkinson, I. and Reynolds, M.: Temporal Logic, vol. I, UP, Oxford, 1994.
Kutschera, F. v.: Causation, Journal of Philosophical Logic 22 (1993), 563–588.
Thomason, R. H.: Combinations of tense and modality, in: Gabbay and Guenthner (1984), 135–165.
Zanardo, A.: A finite axiomatization of the set of strongly valid Ockamist formulas, Journal of Philosophical Logic 14 (1985), 447–468.
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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