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  • Igor Sedlár (ICS CAS):

    Changing the World, Constructively

    17.02.2021 16:00Místnost ZOOM @ Ústav informatiky
    Pod Vodárenskou věží 2
    Praha, 182 00
    Seminář aplikované matematické logiky

    The finite tree property of intuitionistic logic entails completeness with respect to posets where each element, seen as a possibly partial situation, is under a maximal element, seen as a possible world containing the situation. This suggests a natural semantics for intuitionistic modal logic based on posets with a binary relation on the set of maximal elements. In this semantics, truth of modal formulas in a situation is determined by looking at worlds containing the situation and worlds accessible from them. In this paper we study modal logics arising from such a semantics. A general completeness-via-canonicty result is provided and various operations on such posets including filtrations are studied. Differences with respect to intuitionistic modal logics known from the literature are discussed. In the final part a completeness result for a version of intuitionistic propositional dynamic logic based on the framework is obtained and the logic is shown to be decidable.

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