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


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 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

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

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