A Hierarchy of Weak Double Negations

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• 作者：Norihiro Kamide (1)
  
• 关键词：Double negation axiom ; Weak double negation axiom ; Paraconsistent negation ; Cut ; elimination ; Completeness
• 刊名：Studia Logica
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：101
• 期：6
• 页码：1277-1297
• 全文大小：
• 作者单位：Norihiro Kamide (1)
  
  1. Faculty of Information Technology and Business, Cyber University, 4F, 1-11 Kitayamabushi-cho, Shinjuku-ku, Tokyo, 162-0853, Japan
  
• ISSN：1572-8730

文摘

In this paper, a way of constructing many-valued paraconsistent logics with weak double negation axioms is proposed. A hierarchy of weak double negation axioms is addressed in this way. The many-valued paraconsistent logics constructed are defined as Gentzen-type sequent calculi. The completeness and cut-elimination theorems for these logics are proved in a uniform way. The logics constructed are also shown to be decidable.