A Square of Oppositions in Intuitionistic Logic with Strong Negation

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• 作者：François Lepage
• 刊名：Logica Universalis
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：10
• 期：2-3
• 页码：327-338
• 全文大小：625 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Computer Science, general
  Logic
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8300
• 卷排序：10

文摘

In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.KeywordsIntuitionistic logicstrong negationKripke modelssaturated sets