Proof Systems Combining Classical and Paraconsistent Negations

Studia Logica 91 (2):217-238 (2009)
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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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Citations of this work

Modal Multilattice Logic.Norihiro Kamide & Yaroslav Shramko - 2017 - Logica Universalis 11 (3):317-343.
A Hierarchy of Weak Double Negations.Norihiro Kamide - 2013 - Studia Logica 101 (6):1277-1297.

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References found in this work

Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.

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