A Square of Oppositions in Intuitionistic Logic with Strong Negation

Logica Universalis 10 (2-3):327-338 (2016)
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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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10.1007/s11787-016-0144-1

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Francois Lepage
Université de Montréal

Citations of this work

The Vatican Square.Jean-Yves Beziau & Raffaela Giovagnoli - 2016 - Logica Universalis 10 (2-3):135-141.

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Nelson's paraconsistent logics.Seiki Akama - 1999 - Logic and Logical Philosophy 7:101.

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