Studia Logica

, Volume 49, Issue 2, pp 255–272 | Cite as

Kripke semantics for knowledge representation logics

  • Ewa Orłowska
Article

Abstract

This article provides an overview of development of Kripke semantics for logics determined by information systems. The proposals are made to extend the standard Kripke structures to the structures based on information systems. The underlying logics are defined and problems of their axiomatization are discussed. Several open problems connected with the logics are formulated. Logical aspects of incompleteness of information provided by information systems are considered.

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References

  1. [1]
    R. Carnap,Meaning and Necessity, Chicago, 1974.Google Scholar
  2. [2]
    A. Church,A formulation of the logic of sense and denotation, In: P. Henle et al. (eds.),Structure, Method and Meaning, New York, 1951.Google Scholar
  3. [3]
    L. Farinas del Cerro andE. Orłowska,DAL — a logic for data analysis,Theoretical Computer Science 36 (1985), pp. 251–264.Google Scholar
  4. [4]
    G. Frege,Ueber sinn und bedeutung,Zeitschrift fuer Philosophische Kritik 100 (1892), pp. 25–50.Google Scholar
  5. [5]
    G. Gargov,Two completeness theorems in the logic for data analysis, ICS PAS Reports 581. 1986.Google Scholar
  6. [6]
    T. B. Iwiński,Algebraic approach to rough sets,Bulletin of the PAS, Mathematics 35 (1987), pp. 673–683.Google Scholar
  7. [7]
    D. Kaplan,Foundations of Intensional Logic, University of California, Los Angeles, 1964.Google Scholar
  8. [8]
    S. Kripke,Semantical analysis of modal logic I,Zeitschrift fuer Mathematische Logik und Grundlagen der Mathematik 9 (1963), pp. 67–96.Google Scholar
  9. [9]
    R. Montague,Pragmatics, In: R. Klibansky (ed.),Contemporary philosophy-la philosophie contemporaine. Florence, 1968.Google Scholar
  10. [10]
    J. Nieminen,Rough tolerance equality and tolerance black boxes,Fundamenta Informaticae 11 (1988), pp. 289–296.Google Scholar
  11. [11]
    E. Orłowska,Dynamic information systems,Fundamenta Informaticae 5 (1982), pp. 101–118.Google Scholar
  12. [12]
    E. Orłowska,Semantics of vague concepts, In: G. Dorn and P. Weingartner (eds.),Foundations of Logic and Linguistics. Problems and Solutions.Selected Contributions to the 7th International Congress of Logic, Methodology and Philosophy of Science, Salzburg, Plenum Press, New York, 1983, pp. 465–482.Google Scholar
  13. [13]
    E. Orłowska,Logic of nondeterministic information,Studia Logica XLIV (1985), pp. 93–102.Google Scholar
  14. [14]
    E. Orłowska,Logic for reasoning about knowledge,Zeitschrift fuer Mathematische Logik nd Grundlagen der Mathematik, to appear.Google Scholar
  15. [15]
    E. Orłowska,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 Publications 21, Polish Scientific Publishers, Warsaw, 1987, pp. 327–337.Google Scholar
  16. [16]
    E. Orłowska andZ. Pawlak,Representation of nondeterministic information,Theoretical Computer Science 29 (1984), pp. 27–39.Google Scholar
  17. [17]
    Z. Pawlak,Information systems-theoretical foundations,Information Systems 6 (1981), pp. 205–218.Google Scholar
  18. [18]
    Z. Pawlak,Rough sets,International Journal of Computer and Information Sciences 11 (1982), pp. 341–350.Google Scholar
  19. [19]
    J. Pomykała,Approximation operations in approximation space,Bulletin of the PAS, Mathematics 35 (1987), pp. 653–662.Google Scholar
  20. [20]
    V. R. Pratt,Application of modal logic to programming,Studia Logica XXXIX (1980), pp. 255–274.Google Scholar
  21. [21]
    D. Scott,An advice on modal logic, In: K. Lambert (ed.),Philosophical Problems in Logic: Some Recent Developments, Dordrecht, 1970, pp. 143–173.Google Scholar
  22. [22]
    K. Segerberg,Applying modal logic,Studia Logica XXXIX (1980), pp. 275–295.Google Scholar
  23. [23]
    D. Vakarelov,Abstract characterization of some knowledge representation systems and the logic NIL of nondeterministic information, In: D. Skordev (ed.),Mathematical Logic and applications.Proceedings of the 1986 Goedel Conference,Druzhba, Bulgaria, Plenum Press, New York, 1987.Google Scholar
  24. [24]
    D. Vakarelov,Modal logics for knowledge representation, to appear.Google Scholar
  25. [25]
    M. K. Valiev,Bazy dannych i wremiennaja logika,Naucznotechniczeskoje sowieszczenie ‘Logiko-algebraiczeskije modeli predstawlenia znanij’, 1983 (In Russian).Google Scholar
  26. [26]
    J. van Benthem,A Manual of Intensional Logic, Lecture Notes of the Center for the Study of Language and Information. Stanford University, 1985.Google Scholar
  27. [27]
    W. Żakowski,Approximations in the space (U, π),Demonstratio Mathematicae 16 (1983), pp. 761–769.Google Scholar

Copyright information

© Polish Academy of Sciences 1990

Authors and Affiliations

  • Ewa Orłowska
    • 1
  1. 1.Polish Academy of SciencesWarsawPoland

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