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Forthcoming papers
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 | Multi-Valued Models for Cut-Free Modal Logics
Alexander Sakharov
The semantics of modal logics are specified by Kripke models, and the applicability of multi-valued models have not been investigated. Multi-valued models for certain normal modal logics are introduced in this paper. These logics are specified by Gentzen-style sequent calculi in which cut is admissible. Fuzzy truth functions are employed in these models but the truth values of disjunction formulas are recursively defined so that they are dependent on all subformulas. These multi-valued models are defined for a variety of sets of truth values. The central result of this paper is that these models are sound and complete for the aforementioned logics. Similar models are also defined for cut-free monotonic modal logics and for other non-normal modal logics.
July 2026
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