Soft Computing

, Volume 21, Issue 23, pp 7119–7123 | Cite as

A topological duality for monadic MV-algebras

Methodologies and Application

Abstract

Monadic MV-algebras are an algebraic model of first-order infinite-valued Łukasiewicz logic in which only one propositional variable is considered. In this paper, we determine a topological duality for these algebras following well-known P. Halmos’ and H. Priestley’s dualities.

Keywords

Boolean Algebra Distributive Lattice Algebraic Model Propositional Variable Priestley Space 

References

  1. Balbes R, Dwinger P (1974) Distributive lattices. University of Missouri Press, MissouriMATHGoogle Scholar
  2. Chang CC (1958) Algebraic analysis of many valued logics. Trans Am Math Soc 88:476–490Google Scholar
  3. Cignoli R (1991) Quantifiers on distributive lattices. Discrete Math 96:183–197CrossRefMATHMathSciNetGoogle Scholar
  4. Cignoli R, D’Ottaviano I, Mundici D (2000) Algebraic foundations of many-valued reasoning. Trends in Logic Studia Logica Library, vol 7. Kluwer, DordrechtMATHGoogle Scholar
  5. Cornish W, Fowler P (1977) Coproducts of De Morgan algebras. Bull Aust Math Soc 16:1–13CrossRefMATHMathSciNetGoogle Scholar
  6. Di Nola A, Grigolia R (2004) On monadic \(MV\)-algebras. Ann Pure Appl Log 128(1–3):125139MATHMathSciNetGoogle Scholar
  7. Figallo Orellano A (2016) A preliminary study of MV-algebras with two quantifiers which commute. Stud Logica. doi:10.1007/s11225-016-9663-2
  8. Font JM, Rodriguez AJ, Torrens A (1984) Wajsberg algebras. Stochastica 8(1):5–31MATHMathSciNetGoogle Scholar
  9. Halmos PR (1962) Algebraic logic. AMS Chelsea Publishing, New YorkGoogle Scholar
  10. Lattanzi M (2004) Wajsberg algebras with a \(U\)-operator. J Multi-valued Log Soft Comput 10(4):315–338MATHMathSciNetGoogle Scholar
  11. Lattanzi M, Petrovich A (2008) A duality for monadic (n+1)-valued MV-algebras. In: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” congress (Spanish), pp 107–117Google Scholar
  12. Martinez G (1990) The Priestley duality for Wajsberg algebras. Stud Log 49(1):31–46CrossRefMATHMathSciNetGoogle Scholar
  13. Mundici D (1986) Interpretation of AF \(\text{ C }^{\ast }\)-algebras in Lukasiewicz sentential calculus. J Funct Anal 65(1):15–63CrossRefMATHMathSciNetGoogle Scholar
  14. Rodriguez Salas AJ (1980) Un estudio algebraico de los Cálculos Proposicionales de Łukasiewicz, Tesis Doctoral, Universidad de BarcelonaGoogle Scholar
  15. Rutledge JD (1959) A preliminary investigation of the infinitely many-valued predicate calculus. Ph.D. Thesis, Cornell UniversityGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Nacional del SurBuenos AiresArgentina

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