Dually hemimorphic semi-Nelson algebras

Logic Journal of the IGPL 28 (3):316-340 (2020)
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Abstract

Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its subvarieties. In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a dually hemimorphic semi-Nelson algebra through some of its deductive systems.

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
On extensions of intermediate logics by strong negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
On the representation of n4-lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
Nelson algebras through Heyting ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.

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