Twist Structures and Nelson Conuclei

Studia Logica 110 (4):949-987 (2022)
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Abstract

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By applying this representation to the original motivating special cases we bring to the surface their underlying similarities.

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Citations of this work

Fragments of quasi-Nelson: residuation.U. Rivieccio - 2023 - Journal of Applied Non-Classical Logics 33 (1):52-119.

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References found in this work

An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible Falsity.David Nelson - 1950 - Journal of Symbolic Logic 15 (3):228-228.

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