Sesión Lógica y ComputabilidadDiscrete duality for tense SHT-algebras
Cecilia Segura
Instituto de Ciencias Básicas - Universidad Nacional de San Juan, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
In this presentation, we introduce an extension of the discrete duality theory for SHT-algebras to the case of tense SHT-algebras. SHT-algebras constitute an extension of symmetric Heyting algebras and T-rough Heyting algebras. First, a discrete duality is developed between SHT-algebras and a class of relational systems called SHT-frames. Then, we consider the enrichment of these structures by incorporating two tense operators, (G) and (H). Based on this extension, tense SHT-algebras and the corresponding tense SHT-frames are introduced. Finally, a discrete duality between tense SHT-algebras and tense SHT-frames is established, thus extending the previously obtained discrete duality results for SHT-algebras.
Trabajo en conjunto con: Carlos Gallardo (Universidad Nacional del Sur, Argentina) y Gustavo Pelaitay (Universidad Nacional de San Juan, Argentina).
Referencias
[1] Ewa Orłowska, Ingrid Rewitzky, Duality via truth: semantic frameworks for lattice-based logics, Log. J. IGPL 13(4) (2005) 467–490.
[2] E. Orłowska, A. Radzikowska, I. Rewitzky, Dualities for Structures of Applied Logics, Studies in Logic, Mathematical Logic & Foundations, vol.56, College Publications, London, 2015.
[3] Ewa Orłowska, Ingrid Rewitzky, Discrete dualities for Heyting algebras with operators, Fundam. Inform. 81(1–3) (2007) 275–295.
[4] C. Gallardo, A. Ziliani, Symmetrical Heyting algebras of order 3 ×3, Soft Comput. 25 (2021) 8839–8847.
[5] Aldo V. Figallo, Gustavo Pelaitay, Tense operators on De Morgan algebras, Log. J. IGPL 22(2) (2014) 255–267.
[6] Aldo Victorio Figallo, Gustavo Pelaitay, Claudia Sanza, Discrete duality for TSH-algebras, Commun. Korean Math. Soc. 27(1) (2012) 47–56.