Advertisement

Studia Logica

, Volume 66, Issue 2, pp 297–323 | Cite as

Weakly Associative Relation Algebras with Polyadic Composition Operations

  • Vera Stebletsova
Article

Abstract

In this paper we introduced various classes of weakly associative relation algebras with polyadic composition operations. Among them is the class RWA of representable weakly associative relation algebras with polyadic composition operations. Algebras of this class are relativized representable relation algebras augmented with an infinite set of operations of increasing arity which are generalizations of the binary relative composition. We show that RWA is a canonical variety whose equational theory is decidable.

algebraic logic relation algebras relativization representation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Andréka et alii 1994]
    H. AndrÉka, Á, Kurucz, I. NÉmeti, I. Sain and A. Simon, ‘Exactly which logics touched by the dynamic trend are decidable?’, Proceedings of the 9th Amsterdam Colloquium, ILLC, University of Amsterdam, 1994, p. 67-86.Google Scholar
  2. [Andréka, Monk & Németi 1991]
    H. AndrÉka, J.D. Monk and I. NÉmeti (eds.), Algebraic Logic; Proceedings of the 1988 Budapest Conference on Algebraic Logic, North-Holland, Amsterdam, 1991.Google Scholar
  3. [Csirmaz, Gabbay & Rijke 1995]
    L. Csirmaz, D. Gabbay and M. de Rijke (eds.), Logic Colloquium '92, CSLI Publications & FoLLI, 1995.Google Scholar
  4. [Goldblatt 1989]
    R. Goldblatt, ‘Varieties of complex algebras’, Annals of Pure and Applied Logic 44 (1989), 173-242.Google Scholar
  5. [Hirsch & Hodkinson 1997]
    R. Hirsch and I. Hodkinson, ‘Step by step — building representations in algebraic logic’, Journal of Symbolic Logic 62 (1997), 225-279.Google Scholar
  6. [Jónsson 1991]
    B. JÓnsson, ‘The theory of binary relations’, in [Andréka, Monk & Németi 1991], p. 245-292.Google Scholar
  7. [Jónsson 1994]
    B. JÓnsson, ‘On the canonicity of Sahlqvist identities’, Studia Logica 53 (1994), 473-491.Google Scholar
  8. [Jónsson & Tarski 1951]
    B. JÓnsson and A. Tarski, ‘Boolean algebras with operators. Part 1’, American Journal of Mathematics 73 (1951), 891-939.Google Scholar
  9. [Maddux 1982]
    R. Maddux, ‘Some varieties containing relation algebra’, Transactions of the American Mathematical Society 272 (1982), 501-526.Google Scholar
  10. [Marx & Venema 1997]
    M. Marx and Y. Venema, Multidimensional Modal Logic, Kluwer Academic Press, 1997.Google Scholar
  11. [Mikulás 1995]
    Sz. MikulÁs, Taming Logics, Doctoral dissertation, ILLC dissertations series 1995-12, University of Amsterdam.Google Scholar
  12. [Németi 1987]
    I. NÉmeti, ‘Decidability of relation algebras with weakened associativity’, Proc. AMS 100 (1987), 340-344.Google Scholar
  13. [Németi 1995]
    I. NÉmeti, ‘Decidable versions of first order logic and cylindric-relativized set algebras’, in [Csirmaz, Gabbay & de Rijke 1995], p. 47-70.Google Scholar
  14. [de Rijke & Venema 1995]
    M. de Rijke and Y. Venema, ‘Sahlqvist's theorem for Boolean algebras with operators with an application to cylindric algebras’, Studia Logica 54 (1995), 61-78.Google Scholar
  15. [Stebletsova 1996]
    V. Stebletsova, ‘Weakly associative relation algebras with polyadic composition operations’, Technical Report 169, Department of Philosophy, Utrecht University, 1996.Google Scholar
  16. [Tarski & Givant 1987]
    A. Tarski and S. Givant, A Formalization of Set Theory Without Variables, AMS Colloquium Publications, 41 (1987).Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Vera Stebletsova
    • 1
  1. 1.Division of Mathematics and Computer Science Department of AIVrije UniversiteitAmsterdamThe Netherlands

Personalised recommendations