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Studia Logica

, Volume 55, Issue 1, pp 205–228 | Cite as

A duality between Pawlak's knowledge representation systems and bi-consequence systems

  • Dimiter Vakarelov
Article

Abstract

A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.

Keywords

Information System Representation System Mathematical Logic Modal Logic Knowledge Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Benthem J. F. A. K.,Modal Logic and Classical Logic Bibliopolis, Napoly, 1986.Google Scholar
  2. [2]
    Gabbay D.,Semantical considerations in Heyting's Intuitionistic Logic, Synthese Library, v. 148., D. Reydel Publishing Company, Holland, 1981.Google Scholar
  3. [3]
    Hughes G. &M. J. Cresswell,A Companion to Modal Logic Methuen, London, 1984.Google Scholar
  4. [4]
    Orlowska, E., ‘Modal logics in the theory of information systems’,Zeitschrift Für Mathematishe Logic Und Grundlagen Der Mathematik 30(1984) 213–222.Google Scholar
  5. [5]
    Orlowska E., ‘Logic of non-deterministic information’,Studia Logica XLIV(1985), 93–102.Google Scholar
  6. [6]
    Orlowska E., ‘Logic of indiscernibility relations’,ICS PAS Reports 546, 1984 LNCS 208, 1985, 177–186.Google Scholar
  7. [7]
    Orlowska E., ‘Kripke models with relative accessibility relations and their applications to inferences from incomplete information’, in: G. Mirkowska and H. Rasiowa (eds.)Mathematical Problems in Computation Theory Banach Center Publikations 21, Polish Scientific Publishers, Warsaw, 1987, 327–337.Google Scholar
  8. [8]
    Orlowska E., ‘Logic approach to information systems’,Fundamenta Informaticae 8(1988), 359–378.Google Scholar
  9. [9]
    Orlowska E., ‘Kripke semantics for knowledge representation logics’,Studia Logica XLIX, 2(1990), 255–272.Google Scholar
  10. [10]
    Orlowska E., ‘Rough set semantics for nonclassical logics’, manuskript, June 1993.Google Scholar
  11. [11]
    Orlowska E. andZ. Pawlak,Logical foundations of knowledge representation systems, ICS PAS Reports 573, 1984.Google Scholar
  12. [12]
    Orlowska E. andZ. Pawlak, ‘Pepresentation of Nondeterministic Information’,Theoretical Computer Science 29(1984) 27–39.Google Scholar
  13. [13]
    Pawlak Z., ‘Information systems — theoretical foundations’,Information Systems 6(1981), 205–218.Google Scholar
  14. [14]
    Pawlak Z.,Systemy Informacyjne WNT, Warszawa, 1983, In Poish.Google Scholar
  15. [15]
    Pawlak Z.,Rough Sets. Theoretical Aspects of reasoning about Data. Kluwer Academic Publishers, Dordrecht/Boston/London, 1991.Google Scholar
  16. [16]
    Rasiowa H. andR. Sikorski.The mathematics of Metamathematics PWN, Warsaw, 1963.Google Scholar
  17. [17]
    Scott D., ‘Domains for Denotational Semantics’, A corrected and expanded version of a paper prepared forICALP'82, Aarthus, Denmark 1982.Google Scholar
  18. [18]
    Segerberg K.,Essay in Classical Modal Logic, Uppsala, 1971.Google Scholar
  19. [19]
    Segerberg K.,Classical propositional operators Clarendon Press, Oxford, 1982.Google Scholar
  20. [20]
    Slowinski R., (ed.),Intelligent Decision Support, Handbook of Applications and Advances of Rough Sets Theory, Cluver Academic Publishers, 1992.Google Scholar
  21. [21]
    Stone M., ‘Topological Representation of Distributive Lattices and Brouwerian Logics’,Cas. Mat. Fys. No 67, 1937 pp. 1–25.Google Scholar
  22. [22]
    Vakarelov D., ‘Abstract characterization of some knowledge representation systems and the logic NIL of nondeterministic information’, in:Artificial Intelligence II, Methodology, Systems, Applications, Ph. Jorrand and V. Sgurev (eds), North-Holland, 1987.Google Scholar
  23. [23]
    Vakarelov D., ‘S4 and S5 together -S4+5’, in:8th International Congress of Logic, Methodology and Philosophy of Science, LMPS'87, Moscow, USSR, 17–22 August 1987, Abstracts, vol. 5, part 3, 271–274.Google Scholar
  24. [24]
    Vakarelov D., ‘Modal characterization of the classes of finite and infinite quasi-ordered sets’, SU/LAL/preprint No1, 1988,Proc. Summer School and Conference on Mathematical Logic, Heyting'88, Chajka near Varna, Bulgaria, 1988.Google Scholar
  25. [25]
    Vakarelov D., ‘Modal logics for knowledge representation systems’,LNCS 363, 1989, 257–277,Theoretical Computer Science 90(1991) 433–456.Google Scholar
  26. [26]
    Vakarelov D., ‘A modal logic for similarity relations in Pawlak knowledge representation systems’,Fundamenta Informaticae XV (1991), 61–79.Google Scholar
  27. [27]
    Vakarelov D., ‘Logical analysis of positive and nagative similarity relations in property systems’. in:WOCFAI'91, First World Conference in the Fundamentals of Artificial Intelligence, 1–5 July 1991, Paris, France, Proceedings (ed.) Mishel De Glas and Dov Gabbay, pp 491–499.Google Scholar
  28. [28]
    Vakarelov D., ‘Consequence relations and information systems’, in:Intelligent Decision Support, Handbook of Applications and Advances of Rough Sets Theory, (ed.) R. Slowinski, Kluwer Academic Publishers, 1992.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Dimiter Vakarelov
    • 1
  1. 1.Department of Mathematical Logic with Laboratory for Applied LogicSofia UniversitySofiaBulgaria

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