Studia Logica 49 (1):105-126 (1990)
Abstract |
The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H
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DOI | 10.1007/BF00401557 |
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References found in this work BETA
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Amsterdam, Netherlands: Warszawa, Pwn - Polish Scientific Publishers.
Notes on N-Lattices and Constructive Logic with Strong Negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
The Craig Interpolation Theorem for Prepositional Logics with Strong Negation.Valentin Goranko - 1985 - Studia Logica 44 (3):291 - 317.
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Citations of this work BETA
On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
The Lattice of Belnapian Modal Logics: Special Extensions and Counterparts.Sergei P. Odintsov & Stanislav O. Speranski - 2016 - Logic and Logical Philosophy 25 (1):3-33.
Knowledge, Uncertainty and Ignorance in Logic: Bilattices and Beyond.George Gargov - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):195-283.
Behavioral Algebraization of Logics.Carlos Caleiro, Ricardo Gonçalves & Manuel Martins - 2009 - Studia Logica 91 (1):63-111.
Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation.Dimiter Vakarelov - 2005 - Studia Logica 80 (2-3):393-430.
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