Publicación: Implicative twist-structures
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2014-09-03
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info:eu-repo/semantics/openAccess
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Springer Alemania
Resumen
The twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicative twist-structure) obtained as a power of a generalized Boolean algebra, focusing on the implication-negation fragment of the usual algebraic language of twist-structures. We prove that implicative twist-structures form a variety which is semisimple, congruence-distributive, finitely generated, and has equationally definable principal congruences. We characterize the congruences of each algebra in the variety in terms of the congruences of the associated generalized Boolean algebra. We classify and axiomatize the subvarieties of implicative twist-structures. We define a corresponding logic and prove that it is algebraizable with respect to our variety.
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Este es el manuscrito aceptado del artículo. La versión registrada fue publicada por primera vez en Algebra Universalis,(2014) 71, 2, 2014, p. 155-186, está disponible en línea en el sitio web del editor: https://doi.org/10.1007/s00012-014-0272-5
This is the accepted manuscript of the article. The registered version was first published in Algebra Universalis, (2014) 71, 2, 2014, p. 155-186, is available online at the publisher's website: https://doi.org/10.1007/s00012-014-0272-5
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Palabras clave
twist-structure, implicative bilattice, N4-lattice, Nelson lattice, representation, subreducts, algebraic logic
Citación
Umberto Rivieccio, Implicative twist-structures. Algebra Universalis,(2014) 71, 2, 2014, p. 155-186; https://doi.org/10.1007/s00012-014-0272-5
Centro
Facultades y escuelas::Facultad de Filosofía
Departamento
Lógica, Historia y Filosofía de la Ciencia