超协调逻辑(Ⅰ)——传统超协调逻辑研究

Paraconsistent Logic( I ):Studied on Tradictional Paraconsistent Logic

这是一个关于超协调逻辑研究系列的首篇,本文中,我们首先说明超协调逻辑的基本概念及其发展背景,根据对超协调性的分析我们把超协调逻辑分成三类。然后,我们介绍并剖析这三类传统的超协调逻辑的基本结果,指出它们各自的优缺点、存在的问题以及相互关系,并特别地研究了几种传统超协调逻辑与非单调逻辑的关系.

Paraconsistent logics are those theories in which an inconsistent theory can be non-trivial, that is, the logics do not allow to infer every conclusion from a contradictory premise. In this report, we describe a couple of results of the study on paraconsistent logics. Firstly,we outline a paradigm of paraconsistent logics based on the analysis of the paraconsistency. After having studied traditional paraconsistent logics, we introduce a definition of new paraconsistent logic,and present some representive works of definitely new paraconsistent logics. Morever,we provide the definition and results of paracomplete logic which is closely related to paraconsistent logic. Then, we study the logical foundations of paraconsistency from the viewpoint of unification. We propose a unified preferential semantics framework for various paraconsistent logics,and a uniform tableau systems for proof theories of various paraconsistent logics. Furthermore, we compare the relation existing between paraconsistent logic and nonmonotonic logic first invented in artificial intelligence. We emphasize the importance of combining these two logics in an unified logics framework which is paraconsistent and nonmonotonic. Finally, we briefly discuss the applications of paraconsistent logic in computer science and artificial intelligence, with especially study the application of paraconsistent and nonmonotonic logic in the for-malization of commonsense reasoning.