info:eu-repo/semantics/article
Discrete duality for TSH-algebras
Fecha
2012-08Registro en:
Figallo, Aldo Victorio; Pelaitay, Gustavo Andrés; Sanza, Claudia; Discrete duality for TSH-algebras; Korean Mathematical Society; Communications of the Korean Mathematical Society; 27; 1; 8-2012; 47-56
0304-9914
2234-3008
CONICET Digital
CONICET
Autor
Figallo, Aldo Victorio
Pelaitay, Gustavo Andrés
Sanza, Claudia
Resumen
In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.