Abstract
New propositional and first-order paraconsistent logics (called L ω and FL ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L ω and FL ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L ω and FL ω are proved. The cut-elimination theorems for L ω and FL ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems.
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Presented by Yaroslav Shramko and Heinrich Wansing
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Kamide, N. Proof Systems Combining Classical and Paraconsistent Negations. Stud Logica 91, 217–238 (2009). https://doi.org/10.1007/s11225-009-9173-6
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DOI: https://doi.org/10.1007/s11225-009-9173-6