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.
Similar content being viewed by others
References
Akama S.: Nelsons paraconsistent logics. Logic Log. Philos. 7, 101–115 (1999)
Nelson D.: Constructible falsit. J. Symb. Logic 14, 16–26 (1949)
Rasiowa H.: N-lattices and constructive logic with strong negation. Fundam. Math. 46, 61–80 (1958)
Vakarelov D.: Intuitive semantics for some three-valued logics connected with information, contrariety and subcontrariety. Stud. Log. XLVIII, 4, 565–575 (1989)
Vorob’ev N.N.: Constructive propositional calculus with strong negation. (in Russian). Doklady Academii Nauk SSSR 85, 456–468 (1952)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11787-016-0144-1