Abstract
Axiomatic proof/refutation systems for the paraconsistent modal logics: KN4 and KN4.D are presented. The completeness proofs boil down to showing that every sequent is either provable or refutable. By constructing finite tree-type countermodels from refutations, the refined characterizations of these logics by classes of finite tree-type frames are established. The axiom systems also provide decision procedures for these logics.
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Special Issue: On Paraconsistency
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Skura, T. Refutations and Proofs in the Paraconsistent Modal Logics: KN4 and KN4.D. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10102-8
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DOI: https://doi.org/10.1007/s11225-024-10102-8