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International Conference on Rough Sets and Intelligent Systems Paradigms

RSEISP 2007: Rough Sets and Intelligent Systems Paradigms pp 22–28Cite as

Rough Sets and Approximation Schemes

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4585))

Abstract

Approximate reasoning is used in a variety of reasoning tasks in Logic-based Artificial Intelligence. In this abstract we compare a number of such reasoning schemes and show how they relate and differ from the approach of Pawlak’s Rough Sets.

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References

  1. Arenas, M., Bertossi, L.E., Chomicki, J.: Answer sets for consistent query answering in inconsistent databases. Theory and Practice of Logic Programming 3(4-5), 393–424 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  3. Denecker, M., Marek, V., Truszczyński, M.: Uniform semantic treatment of default and autoepistemic logics. Artificial Intelligence Journal 143, 79–122 (2003)

    Article  MATH  Google Scholar 

  4. Denecker, M., Marek, V., Truszczyński, M.: Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation 192, 84–121 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Düntsch, I., Orłowska, E.: Beyond Modalities: Sufficiency and Mixed Algebras. Chapter 16 of [OS01] (2001)

    Google Scholar 

  6. Fitting, M.C.: A Kripke-Kleene semantics for logic programs. Journal of Logic Programming 2(4), 295–312 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings. of the International Joint Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  8. Jonsson, B.: A Survey of Boolean Algebras with Oprators. In: Algebras and Order, pp. 239–284. Kluwer, Dordrecht (1991)

    Google Scholar 

  9. Jonsson, B., Tarski, A.: Boolean Algebras with Operators. American Journal of Mathematics 73, 891–939 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam Fifth reprint (1967)

    Google Scholar 

  11. Kunen, K.: Negation in logic programming. Journal of Logic Programming 4(4), 289–308 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)

    MATH  Google Scholar 

  13. Marek, W., Pawlak, Z.: Information storage and retrieval systems, mathematical foundations. Theoretical Computer Science 1(4), 331–354 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  14. Marek, W., Pawlak, Z.: Rough sets and information systems. Fundamenta Informaticae 7(1), 105–115 (1984)

    MATH  MathSciNet  Google Scholar 

  15. Marek, V.W., Truszczyński, M.: Nonmonotonic Logic; Context-Dependent Reasoning. Springer, Berlin (1993)

    MATH  Google Scholar 

  16. Marek, V.W., Truszczynski, M.: Contributions to the Theory of Rough Sets. Fundamenta Informaticae 39(4), 389–409 (1999)

    MATH  MathSciNet  Google Scholar 

  17. Orłowska, E., Szałas, A.: Relational Methods for Computer Science Applications Selected Papers from In: RelMiCS’98. 4th International Seminar on Relational Methods in Logic, Algebra and Computer Science. Studies in Fuzziness and Soft Computing, vol. 65, Physica-Verlag/Springer, Heidelberg (2001)

    Google Scholar 

  18. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pawlak, Z.: Rough Sets – theoretical aspects of reasoning about data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  20. SanJuan, E., Iturrioz, L.: Duality and informational representability of some information algebras. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, Methodology and Applications, pp. 233–247. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  21. Selman, B., Kautz, H.: Knowledge Compilation and Theory Approximation. Journal of the ACM 43(2), 193–224 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  22. Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA

    Victor W. Marek & Mirosław Truszczynski

Authors
  1. Victor W. Marek
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  2. Mirosław Truszczynski
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Editor information

Marzena Kryszkiewicz James F. Peters Henryk Rybinski Andrzej Skowron

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Marek, V.W., Truszczynski, M. (2007). Rough Sets and Approximation Schemes. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds) Rough Sets and Intelligent Systems Paradigms. RSEISP 2007. Lecture Notes in Computer Science(), vol 4585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73451-2_4

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  • DOI: https://doi.org/10.1007/978-3-540-73451-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73450-5

  • Online ISBN: 978-3-540-73451-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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