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 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of this paper.

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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