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ON CONTRA-CLASSICAL VARIANTS OF NELSON LOGIC N4 AND ITS CLASSICAL EXTENSION

Published online by Cambridge University Press:  24 October 2018

HITOSHI OMORI  and
HEINRICH WANSING
HITOSHI OMORI*
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology
HEINRICH WANSING*
Affiliation:
Department of Philosophy I, Ruhr-Universität Bochum
*
*SCHOOL OF INFORMATION SCIENCE JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY NOMI, JAPAN E-mail: [email protected]URL: https://sites.google.com/site/hitoshiomori/home
†DEPARTMENT OF PHILOSOPHY I RUHR-UNIVERSITÄT BOCHUM BOCHUM, GERMANY E-mail: [email protected]URL: http://www.ruhr-uni-bochum.de/philosophy/logic/
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Abstract

In two recent articles, Norihiro Kamide introduces unusual variants of Nelson’s paraconsistent logic and its classical extension. Kamide’s systems, IP and CP, are unusual insofar as double negations in these logics behave as intuitionistic and classical negations, respectively. In this article we present Hilbert-style axiomatizations of both IP and CP. The axiom system for IP is shown to be sound and complete with respect to a four-valued Kripke semantics, and the axiom system for CP is characterized by four-valued truth tables. Moreover, we note some properties of IP and CP, and emphasize that these logics are unusual also because they are contra-classical and inconsistent but nontrivial. We point out that Kamide’s approach exemplifies a general method for obtaining contra-classical logics, and we briefly speculate about a linguistic application of Kamide’s logics.

Keywords

03B5303B6003B65double negationNelson’s paraconsistent logicHilbert-style axiomatizationscontra-classical logicsfour-valued semanticsnegative concord
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 4 , December 2018 , pp. 805 - 820
Copyright
Copyright © Association for Symbolic Logic 2018 

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