Advertisement

Journal of Philosophical Logic

, Volume 31, Issue 3, pp 211–243 | Cite as

A Theory of Hypermodal Logics: Mode Shifting in Modal Logic

  • D. M. Gabbay
Article

Abstract

A hypermodality is a connective □ whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames.

modal logic combining logic hypermodality frame completeness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Gabbay, D. M.: Investigations in Modal and Tense Logics, Reidel, Dordrecht, 1976.Google Scholar
  2. 2.
    Gabbay, D. M.: Temporal logic and quantifier translations, to appear in U. Reyle (ed.), Festschrift for C. Rohrer, Cambridge University Press.Google Scholar
  3. 3.
    Gabbay, D. M., Hodkinson, I., and Reynolds, M.: Temporal Logic, Volume 1, Oxford University Press, 1994.Google Scholar
  4. 4.
    Gabbay, D. M., Reynolds, M., and Finger, M.: Temporal Logic, Volume 2, Oxford University Press, 2000.Google Scholar
  5. 5.
    Ohlbach, H. J.: Semantic based translation for modal logic, J. Logic Comput. 1 (1990).Google Scholar
  6. 6.
    Sahlqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic, in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland, 1975, pp. 110–143.Google Scholar
  7. 7.
    Gabbay, D. M.: Labelled Deductive Systems, Volume 1, Oxford University Press, 1996.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • D. M. Gabbay
    • 1
  1. 1.Department of Computer SciencesAF King's CollegeLondonUK

Personalised recommendations