Symmetric and dual paraconsistent logics

• Authors: Kamide Norihiro , Wansing Heinrich
• Languages of publication: EN

Abstracts

EN

Two new first-order paraconsistent logics with De Morgan-type negations and co-implication, called symmetric paraconsistent logic (SPL) and dual paraconsistent logic (DPL), are introduced as Gentzen-type sequent calculi. The logic SPL is symmetric in the sense that the rule of contraposition is admissible in cut-free SPL. By using this symmetry property, a simpler cut-free sequent calculus for SPL is obtained. The logic DPL is not symmetric, but it has the duality principle. Simple semantics for SPL and DPL are introduced, and the completeness theorems with respect to these semantics are proved. The cut-elimination theorems for SPL and DPL are proved in two ways: One is a syntactical way which is based on the embedding theorems of SPL and DPL into Gentzen’s LK, and the other is a semantical way which is based on the completeness theorems.

Keywords

EN

symmetric paraconsistent logic; dual paraconsistent logic; sequent calculus; cut-elimination; completeness

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2010
• Volume: 19
• Issue: 1-2
• Pages: 7–30

Dates

published

2010-03-01

Contributors

author

Kamide Norihiro

• Waseda Institute for Advanced Study, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo 169-8050, Japan

author

Wansing Heinrich

• Dresden University of Technology, 01069 Dresden, Germany

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Identifiers

DOI

10.12775/LLP.2010.002