Abstract
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.
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Lepage, F. A Square of Oppositions in Intuitionistic Logic with Strong Negation. Log. Univers. 10, 327–338 (2016). https://doi.org/10.1007/s11787-016-0144-1
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DOI: https://doi.org/10.1007/s11787-016-0144-1