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Relational Attribute Systems II: Reasoning with Relations in Information Structures

  • Ivo Düntsch
  • Günther Gediga
  • Ewa Orłowska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4400)

Abstract

We describe deduction mechanisms for various types of data bases with incomplete information, in particular, relational attribute systems, which we have introduced earlier in [8].

Keywords

Attribute information relation information system  relational attribute system fuzzy information system relational deduction semantical framework. 

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References

  1. 1.
    Allen, J.F.: Maintaining knowledge about temporal intervals. Communications of the ACM 26(11), 832–843 (1983)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bresolin, D., Golińska-Pilarek, J., Orłowska, E.: Relational dual tableaux for interval temporal logics. Journal of Applied Non-Classical Logics 16(3–4), 251–277 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Cottrell, R., Düntsch, I.: An implementation of multivalued information systems. In: Düntsch, I., Winter, M. (eds.) Proceedings of the 8th International Workshop on Relational Methods in Computer Science - RelMiCS’8, St Catharines, pp. 31–36 (2005)Google Scholar
  4. 4.
    Dallien, J.: RelDT: Relational dual tableaux automated theorem prover (2005), Available at http://logic.stfx.ca/reldt/index.html
  5. 5.
    Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  6. 6.
    Düntsch, I.: Relation algebras and their application in temporal and spatial reasoning. Artificial Intelligence Review 23, 315–357 (2005)CrossRefzbMATHGoogle Scholar
  7. 7.
    Düntsch, I., Gediga, G.: Rough set data analysis. In: Encyclopedia of Computer Science and Technology, vol. 43, pp. 281–301. Marcel Dekker, New York (2000)Google Scholar
  8. 8.
    Düntsch, I., Gediga, G., Orłowska, E.: Relational attribute systems. International Journal of Human Computer Studies 55(3), 293–309 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Düntsch, I., Orłowska, E.: A proof system for contact relation algebras. Journal of Philosophical Logic 29, 241–262 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Formisano, A., Nicolosi, M.: An efficient relational deductive system for propositional nonclassical logics. Journal of Applied Non-Classical Logics 16(3–4), 367–408 (2006)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Frias, M., Orłowska, E.: A proof system for fork algebras and its applications to reasoning in logics based on intuitionism. Logique et Analyse, 150–152: 239–284 (1995)Google Scholar
  12. 12.
    Furusawa, H.: Algebraic formalisations of fuzzy relations and their representability. PhD thesis, Kyushu University, Fukuoka (1998)Google Scholar
  13. 13.
    Golińska-Pilarek, J., Orłowska, E.: Relational logics and their applications. In: de Swart, H., et al. (eds.) TARSKI 2006. LNCS (LNAI), vol. 4342, pp. 125–163. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Kawahara, Y., Furusawa, H.: An algebraic formalization of fuzzy relations. Fuzzy Sets and Systems 119, 125–135 (1999)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Lipski, W.: Informational systems with incomplete information. In: Michaelson, S., Milner, R. (eds.) Third International Colloquium on Automata, Languages and Programming, pp. 120–130. Edinburgh University Press, Edinburgh (1976)Google Scholar
  16. 16.
    Lipski, W.: On databases with incomplete information. Journal of the ACM 28, 41–70 (1981)CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    MacCaull, W.: Relational semantics and a relational proof system for the full Lambek calculus. Journal of Symbolic Logic 63(2), 623–637 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    MacCaull, W., Orłowska, E.: Correspondence results for relational proof systems with application to the Lambek calculus. Studia Logica 71(3), 389–414 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    MacCaull, W., Orłowska, E.: A logic of typed relations and its applications to relational databases. To appear in the Journal of Logic and Computation (2005), available at http://logic.stfx.ca/reldt/pubs.html
  20. 20.
    Maddux, R.: Relation algebras for reasoning about time and space. In: Nivat, M., et al. (eds.) Algebraic Methodology and Software Technology (AMAST ’93), Workshops in Computing, pp. 27–44. Springer, New York (1993)Google Scholar
  21. 21.
    Orłowska, E.: Relational interpretation of modal logics. In: Andréka, H., Nemeti, I., Monk, D. (eds.) Algebraic Logic. Colloquia mathematica Societatis Jǎnos Bolyai, vol. 54, pp. 443–471. North-Holland, Amsterdam (1991)Google Scholar
  22. 22.
    Orlowska, E.: Relational semantics for non-classical logics: Formulas are relations. In: Wolenski, J. (ed.) Philosophical Logic in Poland, pp. 167–186. Kluwer Academic Publishers, Dordrecht (1994)Google Scholar
  23. 23.
    Orlowska, E.: Relational proof systems for modal logics. In: Wansing, H. (ed.) Proof Theory of Modal Logic, pp. 55–77. Kluwer Academic Publishers, Dordrecht (1995)Google Scholar
  24. 24.
    Orłowska, E.: Relational formalisation of nonclassical logics. In: Relational Methods in Computer Science. Advances in Computing Science, pp. 90–105. Springer, Wien (1997)Google Scholar
  25. 25.
    Orłowska, E.: Studying incompleteness of information: A class of information logics. In: Kijania-Placek, K., Wolenski, J. (eds.) The Lvov-Warsaw School and Contemporary Philosophy, pp. 283–300. Kluwer, Dordrecht (1998)Google Scholar
  26. 26.
    Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29, 27–39 (1984)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Orłowska, E., Radzikowska, A.: Double residuated lattices and their applications. In: de Swart, H. (ed.) RelMiCS 2001. LNCS, vol. 2561, pp. 177–198. Springer, Heidelberg (2002)Google Scholar
  28. 28.
    Pawlak, Z.: Information systems, theoretical foundations. Information Systems 6, 205–218 (1981)CrossRefzbMATHGoogle Scholar
  29. 29.
    Pawlak, Z.: Rough sets. Internat. J. Comput. Inform. Sci. 11, 341–356 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  30. 30.
    Radzikowska, A., Kerre, E.E.: On some classes of fuzzy information relations. In: IEEE International Symposium on Multiple-Valued Logic (ISMVL), IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
  31. 31.
    Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics. Polska Akademia Nauk. Monografie matematyczne, vol. 41. Polish Scientific Publishers, Warsaw (1963)zbMATHGoogle Scholar
  32. 32.
    Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989), English version: Relations and Graphs. In: Discrete Mathematics for Computer Scientists, EATCS Monographs on Comp. Sci., Springer (1993)zbMATHGoogle Scholar
  33. 33.
    Tarski, A.: On the calculus of relations. Journal of Symbolic Logic 6, 73–89 (1941)CrossRefMathSciNetzbMATHGoogle Scholar
  34. 34.
    Tarski, A.: Introduction to Logic and the Methodology of Deductive Sciences. Oxford University Press, Oxford (1965)zbMATHGoogle Scholar
  35. 35.
    Vakarelov, D.: Modal logics for knowledge representation systems. In: Meyer, A.R., Taitslin, M.A. (eds.) Logic at Botik 1989. LNCS, vol. 363, pp. 257–277. Springer, Heidelberg (1989)Google Scholar
  36. 36.
    Vakarelov, D.: A modal logic for set relations. In: 10th International Congress of Logic, Methodology and Philosophy of Science, Volume of abstracts, Florence (1995)Google Scholar
  37. 37.
    Vakarelov, D.: Information systems, similarity relations, and modal logics. In: Orłowska, E. (ed.) Incomplete Information – Rough Set Analysis, pp. 492–550. Physica, Heidelberg (1998)Google Scholar
  38. 38.
    Winter, M.: A new Algebraic Approach to L-Fuzzy Relations convenient to study Crispness. Information Sciences 139(3–4), 233–252 (2001)CrossRefMathSciNetzbMATHGoogle Scholar
  39. 39.
    Winter, M.: Representation Theory of Goguen Categories. Fuzzy Sets and Systems 138(1), 85–126 (2003)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Ivo Düntsch
    • 1
  • Günther Gediga
    • 2
  • Ewa Orłowska
    • 3
  1. 1.Brock University, St. Catharines, OntarioCanada
  2. 2.University of OsnabrúckGermany
  3. 3.National Institute of Telecommunications, WarsawPoland

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