Journal of Philosophical Logic

, Volume 28, Issue 4, pp 371–398 | Cite as

Combinations of Tense and Modality for Predicate Logic

  • Stefan Wölfl


In recent years combinations of tense and modality have moved into the focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T×W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T×W-semantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed.

tense modality Kamp-semantics T×W-semantics (strong) completeness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Chang, C. C. and Keisler, H. J.: Model Theory, North-Holland, Amsterdam, 1973.Google Scholar
  2. Chellas, B.: “Time and Modality in the Logic of Agency”, Studia Logica 51 (1992), 485–517.Google Scholar
  3. Di Maio, M. C. and Zanardo, A.: “Synchronized Histories in Prior-Thomason Representation of Branching Time”, in: D. M. Gabbay and H. Ohlbach (eds), Proceedings of the First International Conference on Temporal Logic, pp. 265–282, Springer, Berlin, 1994.Google Scholar
  4. Ebbinghaus, H.-D., Flum, J. and Thomas, W.: Einführung in die mathematische Logik, Wiss. Buchges, Darmstadt, 1978.Google Scholar
  5. Gabbay, D. M.: “An Irreflexivity Lemma with Applications to Axiomatizations of Conditions on Tense Frames”, in: Uwe Mönnich (ed.), Aspects of Philosophical Logic, Reidel, Dordrecht, 1981.Google Scholar
  6. Gabbay, D. M., Hodkinson, I. and Reynolds, M.: Temporal Logic; Mathematical Foundations and Computational Aspects, vol. I, Clarendon, Oxford, 1994.Google Scholar
  7. Gargov, G. and Goranko, V.: “Modal Logic with Names”, J. Philos. Logic 22 (1993), 607–636.Google Scholar
  8. Hughes, G. E. and Cresswell, M. J.: A New Introduction toModal Logic,Methuen, London, New York, 1996.Google Scholar
  9. Kutschera, F. v.: “T × W-Completeness”, J. Philos. Logic 26 (1997), 241–250.CrossRefGoogle Scholar
  10. Kutschera, F. v.: “Causation”, J. Philos. Logic 22 (1993), 563–588.Google Scholar
  11. Meixner, U.: Handlung, Zeit, Notwendigkeit, de Gruyter, Berlin, 1987.Google Scholar
  12. Thomason, R. H.: “Combinations of Tense and Modality”, in: D. M. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic, vol. II, Kluwer, Dordrecht, 1984.Google Scholar
  13. Zanardo, A.: “Branching-Time Logic with Quantification over Branches: The Point of View of Modal Logic”, J. Symbolic Logic 61(1) (1996), 1–39.Google Scholar
  14. Zanardo, A.: “A Complete Deductive System for Since-Until Branching-Time Logic”, J. Philos. Logic 20 (1991), 131–148.CrossRefGoogle Scholar
  15. Zanardo, A.: “On the Characterizability of the Frames for the Unpreventability of the Present and the Past”, Notre Dame J. Formal Logic 27 (1986), 556–564.Google Scholar
  16. Zanardo, A.: “A Finite Axiomatization of the Set of Strongly Valid Kampist Frames”, J. Philos. Logic 14 (1985), 447–468.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Stefan Wölfl
    • 1
  1. 1.Institut für Philosophie Universität RegensburgRegensburgGermany

Personalised recommendations