Skip to main content
Springer Nature Link
Log in

States on Polyadic MV-algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

This paper is a contribution to the algebraic logic of probabilistic models of Łukasiewicz predicate logic. We study the MV-states defined on polyadic MV-algebras and prove an algebraic many-valued version of Gaifman’s completeness theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amer M.A.: ‘Probability Logic and Measures on Epimorphic Images of Coproducts of Measurable Spaces’. Rep. Math. Logic 28, 29–52 (1994)

    Google Scholar 

  2. Chang C.C.: ‘Algebraic Analysis of Many Valued Logics’. Trans. Amer. Math. Soc. 88, 467–490 (1958)

    Article  Google Scholar 

  3. Cignoli, R. L.O., I.M. L. D’Ottaviano, and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, 2000.

  4. Daigneault, A., Théorie des modèles en logique mathématique, Montréal, 1967.

  5. Drăgulici D., Georgescu G.: ‘Algebraic Logic for Rational Pavelka Predicate Calculus’. Math. Log. Quart. 47, 315–326 (2001)

    Article  Google Scholar 

  6. Fenstad, J. E., ‘Representation of Probabilities Defined on First Order Languages’, in J. N. Crossley (ed.), Sets, Models and Recursion Theory, North-Holland, 1967, pp. 156-172.

  7. Gaifman H.: ‘Concerning Measures on First Order Calculi’. Israel J. Math. 2, 1–18 (1964)

    Article  Google Scholar 

  8. Georgescu G.: ‘Some Model Theory for Probability Structures’. Rep. Math. Logic 35, 103–113 (2001)

    Google Scholar 

  9. Georgescu G.: ‘Bosbach States on Fuzzy Structures’. Soft Computing 8, 217–230 (2004)

    Google Scholar 

  10. Hájek P., Metamathematics of Fuzzy Logic, Kluwer, 1998.

  11. Halmos P.R.: Algebraic Logic. Chelsea Publ Comp., New York (1962)

    Google Scholar 

  12. Kroupa T.: ‘Representation and Extension of States on MV-algebras’. Arch. Math. Logic 45, 381–392 (2006)

    Article  Google Scholar 

  13. Łukasiewicz J., Tarski A.: ‘Untersuchungen über den Aussagenkalkül’. Comptes Rendus de la Société de Sciences et de Lettres de Varsovie, iii 23, 1–21 (1930)

    Google Scholar 

  14. Mundici D.: ‘Averaging the Truth-Value in Lukasiewicz Logic’. Studia Logica 55(1), 113–127 (1995)

    Article  Google Scholar 

  15. Riečan, B., and D. Mundici, ‘Probability on MV-algebras’, in E. Pap (ed.), Handbook of Measure Theory, I, II, North-Holland, 2002, 869–909.

  16. Riečan, B., and T. Neubrunn, Integral, Measure, and Ordering, Kluwer, 1997.

  17. Schwartz D.: ‘Polyadic MV-algebras’. Zeit. f.Math. Logik und Grundlagen d.Math. 26, 561–564 (1980)

    Article  Google Scholar 

  18. Scott, D., and P. Krauss, ‘Assigning Probabilities to Logical Formulas’, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland, 1966, pp. 219–264.

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014, Bucharest, RO, Romania

    George Georgescu

Authors
  1. George Georgescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George Georgescu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgescu, G. States on Polyadic MV-algebras. Stud Logica 94, 231–243 (2010). https://doi.org/10.1007/s11225-010-9233-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-010-9233-y

Keywords