A Square of Oppositions in Intuitionistic Logic with Strong Negation
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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 logic strong negation Kripke models saturated sets
Mathematics Subject ClassificationPrimary 03B20 Secondary 03B45 03B55 03B60
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- 5.Vorob’ev N.N.: Constructive propositional calculus with strong negation. (in Russian). Doklady Academii Nauk SSSR 85, 456–468 (1952)Google Scholar