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  1. Notes on N-Lattices and Constructive Logic with Strong Negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
  • On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
    In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine the (...)
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  • On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
    N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...)
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  • Nelson Algebras Through Heyting Ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.
    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 (...)
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  • The Class of Extensions of Nelson's Paraconsistent Logic.Sergei P. Odintsov - 2005 - Studia Logica 80 (2-3):291-320.
    The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
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  • Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.