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An Application of Standard BAO Theory to Some Abstract Information Algebras

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Relational Methods for Computer Science Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 65))

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Abstract

We show how methods that were introduced by B. Jónsson and A. Tarski in the paper “Boolean algebras with operators” (1951) are useful to develop representational mechanisms of some abstract algebraic structures related to uncertainty.

Research realized in the framework of COST Action n# 15 (in Informatics) “Many-Valued Logics for Computer Science Applications”

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References

  1. Davey B.A., Priestley H.A. (1990) Introduction to Lattices and Order. Cambridge University Press

    MATH  Google Scholar 

  2. Gehrke M., Jónsson B. (1994) Bounded Distributive Lattices with Operators. Mathematica Japonica 40:207–215

    MathSciNet  MATH  Google Scholar 

  3. Halmos P.R. (1963) Lectures on Boolean algebras. D. Van Nostrand Company

    MATH  Google Scholar 

  4. Jónsson B. (1991) A Survey of Boolean Algebras with Operators. In: Rosenberg I.G. and Sabidussi G. (Eds.) Algebras and Orders, Kluwer Academic Publishers, Dordrecht, 239–284

    Google Scholar 

  5. Jónsson B. (1994) On the Canonicity of Sahlqvist Identities. Studia Logica 53:473–491

    Article  MathSciNet  MATH  Google Scholar 

  6. Jónsson B., Tarski A. (1951–1952) Boolean algebras with operators I and II. American Journal of Mathematics 73:891–939, 74:127–162

    Article  MathSciNet  MATH  Google Scholar 

  7. Kramer R., Maddux R. (1982) Equations not preserved by complete extensions. Algebra Universalis 15:86–89

    Article  MathSciNet  MATH  Google Scholar 

  8. Orlowska E. (1995) Information Algebras, LNCS 936:50–65

    Google Scholar 

  9. Pawlak Z. (1991) Rough Sets. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  10. Ponasse D., Carrega J-C. (1979) Algèbre et topologie Booléennes. Masson, Paris

    MATH  Google Scholar 

  11. Ribeiro H. (1952) A remark on Boolean Algebras with operators, American Journal of Mathematics 74:163–167

    Article  MathSciNet  MATH  Google Scholar 

  12. SanJuan E., Iturrioz L. (1998) Duality and Informational Representability of some Information Algebras. In: Polkowski L. and Skowron A. (Eds.) Rough Sets in Knowledge Discovery, Methodology and Applications, Physica-Verlag, Heidelberg, 233–247

    Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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SanJuan, E., Iturrioz, L. (2001). An Application of Standard BAO Theory to Some Abstract Information Algebras. In: Orłowska, E., Szałas, A. (eds) Relational Methods for Computer Science Applications. Studies in Fuzziness and Soft Computing, vol 65. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1828-4_12

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  • DOI: https://doi.org/10.1007/978-3-7908-1828-4_12

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00362-6

  • Online ISBN: 978-3-7908-1828-4

  • eBook Packages: Springer Book Archive

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