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Completeness of Tableau Calculi for Two-Dimensional Hybrid Logics (2210.09630v4)
Published 18 Oct 2022 in math.LO and cs.LO
Abstract: Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau calculus for hybrid dependent product logic (HdPL), where one dimension depends on the other. In addition, we add a special rule to the tableau calculus for HdPL and show that it is still sound and complete. All of them lack termination, however.