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Studia Logica

, Volume 91, Issue 2, pp 217–238 | Cite as

Proof Systems Combining Classical and Paraconsistent Negations

  • Norihiro KamideEmail author
Article

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.

Keywords

Paraconsistent negation sequent calculus cut-elimination completeness 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan

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