Logica Universalis

, Volume 10, Issue 2–3, pp 327–338

A Square of Oppositions in Intuitionistic Logic with Strong Negation


DOI: 10.1007/s11787-016-0144-1

Cite this article as:
Lepage, F. Log. Univers. (2016) 10: 327. doi:10.1007/s11787-016-0144-1


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.


Intuitionistic logic strong negation Kripke models saturated sets 

Mathematics Subject Classification

Primary 03B20 Secondary 03B45 03B55 03B60 

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Département de philosophieUniversité de MontréalMontréalCanada

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