## Kripke semantics for knowledge representation logics.(English)Zbl 0726.03023

The author shows how Kripke structures are determined by information systems, which then enables us to provide modal logics for knowledge representation in a natural way. She discusses the axiomatization of logics thus defined and extends the Kripke modeling in order to deal with temporal aspects of information or to give reasonings about objects and their properties.

### MSC:

 03B60 Other nonclassical logic 68T30 Knowledge representation 68T27 Logic in artificial intelligence 03B45 Modal logic (including the logic of norms) 03B80 Other applications of logic
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### References:

 [1] R. Carnap,Meaning and Necessity, Chicago, 1974. [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. · Zbl 0054.00601 [3] L. Farinas del Cerro andE. Orłowska,DAL – a logic for data analysis,Theoretical Computer Science 36 (1985), pp. 251–264. · Zbl 0565.68032 [4] G. Frege,Ueber sinn und bedeutung,Zeitschrift fuer Philosophische Kritik 100 (1892), pp. 25–50. [5] G. Gargov,Two completeness theorems in the logic for data analysis, ICS PAS Reports 581. 1986. [6] T. B. Iwiński,Algebraic approach to rough sets,Bulletin of the PAS, Mathematics 35 (1987), pp. 673–683. [7] D. Kaplan,Foundations of Intensional Logic, University of California, Los Angeles, 1964. · Zbl 0126.12002 [8] S. Kripke,Semantical analysis of modal logic I,Zeitschrift fuer Mathematische Logik und Grundlagen der Mathematik 9 (1963), pp. 67–96. · Zbl 0118.01305 [9] R. Montague,Pragmatics, In: R. Klibansky (ed.),Contemporary philosophy-la philosophie contemporaine. Florence, 1968. [10] J. Nieminen,Rough tolerance equality and tolerance black boxes,Fundamenta Informaticae 11 (1988), pp. 289–296. · Zbl 0649.68115 [11] E. Orłowska,Dynamic information systems,Fundamenta Informaticae 5 (1982), pp. 101–118. [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. [13] E. Orłowska,Logic of nondeterministic information,Studia Logica XLIV (1985), pp. 93–102. · Zbl 0575.03018 [14] E. Orłowska,Logic for reasoning about knowledge,Zeitschrift fuer Mathematische Logik nd Grundlagen der Mathematik, to appear. · Zbl 0641.68160 [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. [16] E. Orłowska andZ. Pawlak,Representation of nondeterministic information,Theoretical Computer Science 29 (1984), pp. 27–39. · Zbl 0537.68098 [17] Z. Pawlak,Information systems-theoretical foundations,Information Systems 6 (1981), pp. 205–218. · Zbl 0462.68078 [18] Z. Pawlak,Rough sets,International Journal of Computer and Information Sciences 11 (1982), pp. 341–350. · Zbl 0501.68053 [19] J. Pomykała,Approximation operations in approximation space,Bulletin of the PAS, Mathematics 35 (1987), pp. 653–662. · Zbl 0642.54002 [20] V. R. Pratt,Application of modal logic to programming,Studia Logica XXXIX (1980), pp. 255–274. · Zbl 0457.03013 [21] D. Scott,An advice on modal logic, In: K. Lambert (ed.),Philosophical Problems in Logic: Some Recent Developments, Dordrecht, 1970, pp. 143–173. · Zbl 0295.02013 [22] K. Segerberg,Applying modal logic,Studia Logica XXXIX (1980), pp. 275–295. · Zbl 0457.03014 [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. [24] D. Vakarelov,Modal logics for knowledge representation, to appear. · Zbl 0755.68131 [25] M. K. Valiev,Bazy dannych i wremiennaja logika,Naucznotechniczeskoje sowieszczenie ’Logiko-algebraiczeskije modeli predstawlenia znanij’, 1983 (In Russian). [26] J. van Benthem,A Manual of Intensional Logic, Lecture Notes of the Center for the Study of Language and Information. Stanford University, 1985. [27] W. \.Zakowski,Approximations in the space (U, {$$\pi$$}),Demonstratio Mathematicae 16 (1983), pp. 761–769. · Zbl 0553.04002
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