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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)
  • 투고 : 2010.09.21
  • 발행 : 2012.01.31

초록

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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참고문헌

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피인용 문헌

  1. An algebraic axiomatization of the Ewald’s intuitionistic tense logic vol.18, pp.10, 2014, https://doi.org/10.1007/s00500-014-1317-6
  2. Tense operators on De Morgan algebras vol.22, pp.2, 2014, https://doi.org/10.1093/jigpal/jzt024
  3. Characterizing intermediate tense logics in terms of Galois connections vol.22, pp.6, 2014, https://doi.org/10.1093/jigpal/jzu024
  4. Tense operators in fuzzy logic vol.276, 2015, https://doi.org/10.1016/j.fss.2014.09.007
  5. Subdirectly Irreducible IKt-Algebras vol.105, pp.4, 2017, https://doi.org/10.1007/s11225-017-9707-2
  6. Duality Results for (Co)Residuated Lattices pp.1661-8300, 2019, https://doi.org/10.1007/s11787-018-0217-4
  7. Principal and Boolean Congruences on $$\varvec{IKt}$$IKt-Algebras vol.106, pp.4, 2018, https://doi.org/10.1007/s11225-017-9770-8