弗完全模态逻辑及其逻辑特性  

Paracomplete Modal Logic Systems and Their Logic Characteristics

作　　者：郝旭东[1] HAO Xu-dong(Department of Philosophy,East China Normal University,Shanghai 200241,China)

机构地区：[1]华东师范大学哲学系,上海200241

出　　处：《湖南科技大学学报（社会科学版）》2022年第5期45-54,共10页Journal of Hunan University of Science and Technology(Social Science Edition)

基　　金：国家社会科学基金重大项目(18ZDA031)。

摘　　要：P_(1)是一个基本的弗完全逻辑系统,其重要特征是排中律在一般意义上无效,并且有些会导致矛盾扩散的逻辑原则在其中失效,从而使得弗完全逻辑具有可以容纳矛盾冲突,但不会导致整个系统无意义的逻辑特性。在系统P_(1)的基础上,通过直接的逻辑扩充可以建立一系列弗完全模态逻辑系统,即P_(1)K,P_(1)D,P_(1)T,P_(1)4,P_(1)G,并可证明它们的可靠性和完全性。这些具有弗完全性质的模态逻辑系统,都具有容忍“真矛盾”的能力。P_(1)is a basic paracomplete logic system,in which the law of excluded middle is invalid in the general sense,and some of the logical principles that lead to the explosive result of true contradictions fail in it.This makes paracomplete logic have certain logical characteristics that can tolerate some contradictions and conflicts,but simultaneously will not make the whole system become meaningless.Based on P_(1),a series of paracomplete modal logic systems,i.e.P_(1)K,P_(1)D,P_(1)T,P_(1)4,P_(1)G can be constructed by logically expanding,and their soundness and completeness can also be proved.It can be shown that these modal logic systems with paracomplete property have the ability to tolerate“true contradictions”.

关 键 词：弗完全 排中律 模态逻辑 真矛盾 悖论 

分 类 号：B81[哲学宗教—逻辑学]