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.
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Gabbay, D.M. A Theory of Hypermodal Logics: Mode Shifting in Modal Logic. Journal of Philosophical Logic 31, 211–243 (2002). https://doi.org/10.1023/A:1015782031903
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DOI: https://doi.org/10.1023/A:1015782031903