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Residuated Kleene Algebras

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Logic and Program Semantics

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7230))

Abstract

We show that there is no finitely axiomatizable class of algebras that would serve as an analogue to Kozen’s class of Kleene algebras if we include the residuals of composition in the similarity type of relation algebras.

Research supported by the Hungarian National Foundation for Scientific Research grant No. T81188.

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References

  1. Andréka, H.: Representation of distributive lattice-ordered semigroups with binary relations. Algebra Universalis 28, 12–25 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andréka, H., Mikulás, S.: Axiomatizability of positive algebras of binary relations. Algebra Universalis 66(1), 7–34 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Andréka, H., Mikulás, S., Németi, I.: The equational theory of Kleene lattices. Theoretical Computer Science 412, 7099–7108 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall (1971)

    Google Scholar 

  5. Crvenković, S., Dolinka, I., Ésik, Z.: The variety of Kleene algebras with conversion is not finitely based. Theoretical Computer Science 230, 235–245 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ésik, Z., Bernátsky, L.: Equational properties of Kleene algebras of relations with conversion. Theoretical Computer Science 137, 237–251 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hirsch, R., Mikulás, S.: Positive reducts of relevance logic and algebras of binary relations. Review of Symbolic Logic 4(1), 81–105 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jipsen, P.: From semirings to residuated Kleene lattices. Studia Logica 76(2), 291–303 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Information and Computation 110, 366–390 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kozen, D.: On action algebras. In: van Eijck, J., Visser, A. (eds.) Logic and Information Flow, pp. 78–88. MIT Press (1994)

    Google Scholar 

  11. Maddux, R.D.: Non-finite-axiomatizability results for cylindric and relation algebras. Journal of Symbolic Logic 54(3), 951–974 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mikulás, S.: On representable ordered residuated semigroups. Logic Journal of the IGPL 19(1), 233–240 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pratt, V.: Action Logic and Pure Induction. In: van Eijck, J. (ed.) JELIA 1990. LNCS, vol. 478, pp. 97–120. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  14. Redko, V.N.: On defining relations for the algebra of regular events. Ukrain. Mat. Z. 16, 120–126 (1964) (in Russian)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13–15 Reáltanoda u., 1053, Budapest, Hungary

    Hajnal Andréka & István Németi

  2. Department of Computer Science and Information Systems, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK

    Szabolcs Mikulás

Authors
  1. Hajnal Andréka
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  2. Szabolcs Mikulás
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  3. István Németi
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Editor information

Editors and Affiliations

  1. Computer Science Department, Cornell University, 4149 Upson Hall, 14853, Ithaca, NY, USA

    Robert L. Constable

  2. Intelligent Systems Faculty of Science, Institute for Computing and Information Sciences, Radboud University Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Alexandra Silva

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Andréka, H., Mikulás, S., Németi, I. (2012). Residuated Kleene Algebras. In: Constable, R.L., Silva, A. (eds) Logic and Program Semantics. Lecture Notes in Computer Science, vol 7230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29485-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-29485-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29484-6

  • Online ISBN: 978-3-642-29485-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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