Studia Logica

, Volume 88, Issue 2, pp 215–231 | Cite as

Three-Valued Temporal Logic Qt and Future Contingents



Prior’s three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic Qt and give its axiomatization and semantics. We also argue that Qt provides a smooth solution to the problem of future contingents.


Prior Q three-valued temporal logic Qt Kripke semantics future contingents 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akama, S., and Nagata, Y., ‘On Prior’s three-valued modal logic Q’, Proc. of ISMVL’ 2005, 2005, pp. 14–19.Google Scholar
  2. Akama, S., Nagata, Y., and Yamada, C., ‘A three-valued temporal logic for future contingents’, to appear in Logique et Analyse, 2007.Google Scholar
  3. Anscombe, G., ‘Aristotle and the sea-battle, De Interpretatione Chapter IX’, Mind LXV: 257, 1956, pp. 1–15.Google Scholar
  4. Aristotle, De Interpretatione, translated by E.M. Edghill, W.D. Ross (ed.), The Works of Aristotle, Oxford University Press, Oxford, 1963.Google Scholar
  5. Blamey P. (1986). ‘Partial logic’. In: Gabbay D., Guenthner F. (eds) Handbook of Philosophical Logic Vol III. Reidel, Dordrecht, pp. 1–70Google Scholar
  6. Bruns, G. and Godefroid, P., ‘Generalized model checking: reasoning about partial state spaces’, Proc. of CONCUR’2000, Springer-Verlag, Berlin, 2000, pp. 168–182.Google Scholar
  7. Bull R.A. (1964). ‘An axiomatization of Prior’s modal calculus Q’, Notre Dame Journal of Formal Logic. 5: 211–214CrossRefGoogle Scholar
  8. Bull R.A. (1965). ‘A modal extension of intuitionistic logic’. Notre Dame Journal of Formal Logic. 6: 142–146CrossRefGoogle Scholar
  9. Correia F. (1999). ’Adequacy results from some Priorean modal logic’. Notre Dame Journal of Formal Logic. 40: 236–249CrossRefGoogle Scholar
  10. Ewald W. (1986). ‘Intuitionistic tense and modal logic’. The Journal of Symbolic Logic. 51: 166–179CrossRefGoogle Scholar
  11. van Fraassen B.(1966). ‘Singular terms, truth-value gaps, and free logic’. Journal of Philosophy. 63: 481–495CrossRefGoogle Scholar
  12. Haack S. (1978). Philosophy of Logics, Cambridge University Press, CambridgeGoogle Scholar
  13. Lukasiewicz, J., ‘On 3-valued logic’, 1920, S.McCall (ed.), Polish Logic, Oxford University Press, Oxford, 1967, pp. 16–18.Google Scholar
  14. Prior A.N.(1957). Time and Modality. Oxford University Press, Oxford.Google Scholar
  15. Prior A.N.(1967). Past, Present and Future. Clarendon Press, Oxford.Google Scholar
  16. Simpson, A., The Proof Theory and Semantics of Intuitionistic Modal Logic, Ph.D. Thesis, Edinburgh, 1993.Google Scholar
  17. Surowik D.(2005). ‘The different methods of rejection of the thesis of determinism in temporal logical systems’. Bulletin of Symbolic Logic. 11: 296–297Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Seiki Akama
    • 1
  • Yasunori Nagata
    • 2
  • Chikatoshi Yamada
    • 3
  1. 1.Kawasaki-shiJapan
  2. 2.Department of Electrical and Electronics EngineeringUniversity of RyukyusOkinawaJapan
  3. 3.Takushoku University Hokkaido CollegeHokkaidoJapan

Personalised recommendations