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Logic and Logical Philosophy

Symmetric and dual paraconsistent logics
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Symmetric and dual paraconsistent logics

Authors

  • Norihiro Kamide Waseda Institute for Advanced Study, Tokyo
  • Heinrich Wansing Dresden University of Technology https://orcid.org/0000-0002-0749-8847

DOI:

https://doi.org/10.12775/LLP.2010.002

Keywords

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

Abstract

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.

References

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Logic and Logical Philosophy

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Published

2010-06-30

How to Cite

1.
KAMIDE, Norihiro and WANSING, Heinrich. Symmetric and dual paraconsistent logics. Logic and Logical Philosophy. Online. 30 June 2010. Vol. 19, no. 1-2, pp. 7-30. [Accessed 5 July 2025]. DOI 10.12775/LLP.2010.002.
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Vol. 19 No. 1-2 (2010)

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