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Hyperintensional Modal Logic: Motivation, Semantic Frameworks, and Basic Theory.
Dragonová, Ivana ; Sedlár, Igor (advisor) ; Punčochář, Vít (referee)
A modal operator is hyperintensional if it does not respect the Equivalence Rule (RE), according to which if two formulas are logically equivalent, then so are the results of applying the modal operator to them. Typically, this happens when dealing with topics finer-grained than propositions, such as the notions of knowledge and belief. This thesis discusses the class of modal logics not closed under (RE) called hyperintensional modal logics and gives an overview of the semantic approaches one can use to give a suitable interpretation for this class of logics. We discuss a state-based approach first introduced by Rantala(1982) and later developed by Wansing(1990) and a structuralist approach proposed by Cresswell(1975). In the final part, we discuss a recent approach by Sedlár (2021), Pascucci and Sedlár (2023), and show that the above-mentioned state-based and structuralist approaches can both be modeled within Sedlár's hyperintensional models. We prove completeness results for the discussed hyperintensional semantic frameworks - all of them are sound and complete with respect to the smallest (hyperintensional) modal logic. 1
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