A theory of hypermodal logics: Mode shifting in modal logic (Q1610618)

Hypermodal logics contain modalities whose nature changes depending on their appearance in a formula. In this paper, the author shows that hypermodal logics are much more expressive than traditional modal logics. The main example is a hypermodal logic shifting between \({\mathbf K}\) and \({\mathbf T}\) modalities which is not complete for any class of Kripke or neighbourhood frames. The author also discusses the relationship of hypermodality, many-dimensional logics and multimodal logics.