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DISCRETE DUALITY FOR TSH-ALGEBRAS

  • Figallo, Aldo Victorio (Departamento de Matem atic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan) ;
  • Pelaitay, Gustavo (Departamento de Matematic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan) ;
  • Sanza, Claudia (Departamento de Matematic Universidad Nacional del Sur, Instituto de Ciencias Basica Universidad Nacional de San Juan)
  • Received : 2010.09.21
  • Published : 2012.01.31

Abstract

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.

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