Abstract
Approximate reasoning is used in a variety of reasoning tasks in logic-based artificial intelligence. In this paper we present several such reasoning schemes and show how they relate and differ from the approach of Pawlak’s Rough Sets.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1992)
Denecker, M., Marek, V., Truszczyński, M.: Uniform semantic treatment of default and autoepistemic logics. Artificial Intelligence Journal 143, 79–122 (2003)
Denecker, M., Marek, V., Truszczyński, M.: Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation 192, 84–121 (2004)
Düntsch, I., Orłowska, E.: Beyond Modalities: Sufficiency and Mixed Algebras. In: Chapter 16 of [OS01] (2001)
Fitting, M.C.: A Kripke-Kleene semantics for logic programs. Journal of Logic Programming 2(4), 295–312 (1985)
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)
Hughes, G.E., Cresswell, M.J.: An Introduction to Modal Logic, Methuen (1968)
Iwiński, T.: Rough analysis in lattices. Working papers of the University of Carlos III, Madrid, Num., 91–23 (1991)
Järvinen, J.: Lattice Theory for Rough Sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)
Jonsson, B.: A Survey of Boolean Algebras with Operators. In: Algebras and Order, pp. 239–284. Kluwer, Dordrecht (1991)
Jonsson, B., Tarski, A.: Boolean Algebras with Operators. American Journal of Mathematics 73, 891–939 (1951)
Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1967) (fifth reprint)
Kunen, K.: Negation in logic programming. Journal of Logic Programming 4(4), 289–308 (1987)
Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)
Marek, W., Pawlak, Z.: Information storage and retrieval systems, mathematical foundations. Theoretical Computer Science 1(4), 331–354 (1976)
Marek, W., Pawlak, Z.: Rough sets and information systems. Fundamenta Informaticae 7(1), 105–115 (1984)
Marek, V.W., Truszczyński, M.: Nonmonotonic Logic; Context-Dependent Reasoning. Springer, Berlin (1993)
Marek, V.W., Truszczyński, M.: Contributions to the Theory of Rough Sets. Fundamenta Informaticae 39(4), 389–409 (1999)
Orłowska, E., Szałas, A.: Relational Methods for Computer Science Applications. In: Selected Papers from 4th International Seminar on Relational Methods in Logic, Algebra and Computer Science (RelMiCS 1998); Studies in Fuzziness and Soft Computing, vol. 65. Physica-Verlag, Springer (2001)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets – theoretical aspects of reasoning about data. Kluwer, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177(1), 28–40
Rasiowa, H.: An Algebraic Introduction to Non-classical Logics. North-Holland, Amsterdam (1974)
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 (1998)
Selman, B., Kautz, H.: Knowledge Compilation and Theory Approximation. Journal of the ACM 43(2), 193–224 (1996)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Marek, V.W., Truszczyński, M. (2008). Approximation Schemes in Logic and Artificial Intelligence. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-89876-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89875-7
Online ISBN: 978-3-540-89876-4
eBook Packages: Computer ScienceComputer Science (R0)