[1]ZHANG Jincheng.A logic system which accommodates contradictions and paradoxes[J].CAAI Transactions on Intelligent Systems,2012,7(3):206-213.
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A logic system which accommodates contradictions and paradoxes

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 7 Number of periods: 2012 3 Page number: 206-213 Column: 学术论文—人工智能基础 Public date: 2012-06-25
Title:
A logic system which accommodates contradictions and paradoxes
Author(s):
ZHANG Jincheng
Correspondence School of the C.P.C. Central Party School, Guangde 242200, China
Keywords:
logic system;  contradiction;  paradox;  positive field;  inverse field;  fixed field;  paraconsistent logic system
CLC:
TP18; O141
DOI:
-
Abstract:
The insufficiencies of various currently used logic systems which accommodate contradictions were analyzed in this paper. The concepts of a positive field, inverse field, and fixed field were put forward, and the paradox was found to be the fixed point in the field of logical thinking. A new logic system S accommodating the contradictions and a semantic model of the system S were built, and then the metatheorem of system S was proven. In the system S, the propositional calculus was divided into three separate fields. All the schemes of calculus and theorems of classical logic were valid in the positive or inverse fields. The paradox, including the contradiction nature, could be proven as a theorem in the fixed field. Compared with the Da Costa paraconsistent logic system Cn, the system S can not only accommodate the contradictions, but also interpret them clearly. Based on this logic system, a foundation of mathematics which accommodates contradictions can be established. 
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Last Update: 2012-09-05

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