Rough Pragmatic Description Logic

  • Zbigniew Bonikowski
  • Edward Bryniarski
  • Urszula Wybraniec-Skardowska

Abstract

In this chapter, a rough description logic is built on the basis of a pragmatic standpoint of representation of knowledge. The pragmatic standpoint has influenced the acceptance of a broader definition of the semantic network than that appearing in the literature. The definition of the semantic network is a motivation of the introduced semantics of the language of the descriptive logic. First, the theoretical framework of representation of knowledge that was proposed in the papers [24,25] is adjusted to the description of data processing. The pragmatic system of knowledge representation is determined, as well as situations of semantic adequacy and semantic inadequacy for represented knowledge are defined. Then, it is shown that general information systems (generalized information systems in Pawlak’s sense) presented in the paper [5] can be interpreted in pragmatic systems of knowledge representation. Rough sets in the set-theoretical framework proposed in papers [7,8] are defined for the general information systems. The pragmatic standpoint about objects is also a motivation to determine a model of semantic network. This model is considered as a general information system. It determines a formal language of the descriptive logic. The set-theoretical framework of rough sets, which was introduced for general information systems, makes it possible to describe the interpretation of this language in the theory of rough sets. Therefore this interpretation includes situations of semantic inadequacy. At the same time, for the class of all interpretations of this type, there exists a certain descriptive logic, which — in this chapter — is called rough pragmatic description logic.

Keywords

Pragmatic knowledge representation semantically adequate knowledge vague knowledge pragmatic information system generalized pragmatic information system rough set semantic network description logic rough pragmatic descriptive logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic. HandbookTheory, Implementation and Application. Cambridge University Press, Cambridge (2003)Google Scholar
  2. 2.
    Bobillo, F., Straccia, U.: fuzzyDL: An expressive fuzzy description logic reasoner. In: Proc. IEEE Int. Conference on Fuzzy Systems FUZZ-IEEE 2008 (IEEE World Congress on Computational Intelligence), pp. 923–930 (2008)Google Scholar
  3. 3.
    Bonikowski, Z.: Algebraic structures of rough sets. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 242–247. Springer (1994)Google Scholar
  4. 4.
    Bonikowski, Z.: Algebraic structures of rough sets in representative approximation spaces. Electr. Notes Theor. Comput. Sci. 82(4) (2003), doi:10.1016/S1571-0661(04)80705-9Google Scholar
  5. 5.
    Bonikowski, Z., Wybraniec-Skardowska, U.: Vagueness and Roughness. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 1–13. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Extensions and intensions in the rough set theory. J. Inform. Sciences 107, 149–167 (1998)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Bryniarski, E.: A calculus of rough sets of the first order. Bull. Pol. Ac.: Math. 37, 109–136 (1989)MathSciNetGoogle Scholar
  8. 8.
    Bryniarski, E.: Formal conception of rough sets. Fund. Infor. 27(2-3), 103–108 (1996)MathSciNetGoogle Scholar
  9. 9.
    Demri, S.P., Orłowska, E.S.: Incomplete Information: Structure, Inference, Complexity. Springer, Heidelberg (2002)MATHGoogle Scholar
  10. 10.
    Fanizzi, N., d’Amato, C., Esposito, F., Lukasiewicz, T.: Representing uncertain concepts in rough description logics via contextual indiscernibility relations. In: Bobillo, F., da Costa, P.C.G., d’Amato, C., et al. (eds.) Proc. 4th Int. Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2008). CEUR-WS, 423. CEUR-WS.org (2008), http://ceur-ws.org/Vol-423/paper7.pdf (cited May 13, 2011)
  11. 11.
    Keet, C.M.: Ontology Engineering with Rough Concepts and Instances. In: Cimiano, P., Pinto, H.S. (eds.) EKAW 2010. LNCS (LNAI), vol. 6317, pp. 503–513. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Kowalski, R.A.: Logic for Problem Solving. North Holland, New York (1979)MATHGoogle Scholar
  13. 13.
    Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theor. Computer Science 29, 27–39 (1984)CrossRefGoogle Scholar
  14. 14.
    Pawlak, Z.: Information systems – Theoretical foundations. Inform. Systems 6, 205–218 (1981)MATHCrossRefGoogle Scholar
  15. 15.
    Pawlak, Z.: Rough sets. Intern. J. Comp. Inform. Sci. 11, 341–356 (1982)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about. Data. Kluwer Academic Publishers, Dordrecht (1991)MATHCrossRefGoogle Scholar
  17. 17.
    Pawlak, Z.: Rough set elements. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1. Methodology and Applications, pp. 10–30. Springer, Heidelberg (1998)Google Scholar
  18. 18.
    Polkowski, L.: Reasoning by Parts. An Outline of Rough Mereology. Warszawa (2011)Google Scholar
  19. 19.
    Skowron, A., Polkowski, L.: Rough mereology and analytical morphology. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 399–437. Springer, Heidelberg (1996)Google Scholar
  20. 20.
    Skowron, A., Wasilewski, P.: An Introduction to Perception Based Computing. In: Kim, T.-h., Lee, Y.-h., Kang, B.-H., Ślęzak, D. (eds.) FGIT 2010. LNCS, vol. 6485, pp. 12–25. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Simou, N., Stoilos, G., Tzouvaras, V., Stamou, G., Kollias, S.: Storing and querying fuzzy knowledge in the semantic web. In: Bobillo, F., da Costa, P.C.G., d’Amato, C., et al. (eds.) Proc. 4th Int. Workshop on Uncertainty Reasoning for the Semantic Web URSW 2008, May 13. CEUR-WS, vol. 423, CEUR-WS.org (2008), http://ceur-ws.org/Vol-423/paper8.pdf (cited May 13, 2011)
  22. 22.
    Simou, N., Mailis, T., Stoilos, G., Stamou, S.: Optimization techniques for fuzzy description logics. In: Description Logics. Proc. 23rd Int. Workshop on Description Logics (DL 2010). CEUR-WS, vol. 573, CEUR-WS.org (2010), http://ceur-ws.org/Vol-573/paper_25.pdf (cited May 13, 2011)
  23. 23.
    Turing, A.M.: Computing machinery and intelligence. Mind 59(236), 433–460 (1950)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Wybraniec-Skardowska, U.: Meaning and interpretation. Studia Logica 85, 107–134 (2007)Google Scholar
  25. 25.
    Wybraniec-Skardowska, U.: On meta-knowledge and truth. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy. Trends in Logic, vol. 28, pp. 319–343. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Żakowski, W.: Approximations in the space (U, Π). Demonstratio Math. 16, 761–769 (1983)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Zbigniew Bonikowski
    • 1
  • Edward Bryniarski
    • 1
  • Urszula Wybraniec-Skardowska
    • 2
  1. 1.Institute of Mathematics and InformaticsOpole UniversityOpolePoland
  2. 2.Group of Logic, Language and InformationOpole UniversityOpolePoland

Personalised recommendations