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We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work [21, 32, 22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are t (true), f (false), i (inconsistent) and u (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.
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Czasopismo
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Tom
Strony
405--438
Opis fizyczny
Bibliogr. 32 poz., tab., wykr.
Twórcy
autor
autor
autor
- Department of Science and Technology, Linköping University, S 601 74 Norrk¨oping, Sweden, aidvi@itn.liu.se.
Bibliografia
- [1] Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases, Addison-Wesley Pub. Co., 1996.
- [2] Alcântara, J., Damásio, C., Pereira, L.: An encompassing framework for Paraconsistent Logic Programs, J. Applied Logic, 3(1), 2005, 67-95.
- [3] Amo, S., Pais, M.: A Paraconsistent Logic Approach for Querying Inconsistent Databases, International Journal of Approximate Reasoning, 46, 2007, 366-386.
- [4] Andersson, R., Vitória, A., Małuszyński, J., Komorowski, J.: RoSy: A Rough Knowledge Base System., RSFDGrC (2), Lecture Notes in Computer Science, vol. 3642 of Lecture Notes in Computer Science, Springer, 2005, 48-58.
- [5] Arieli, O., Avron, A.: The Value of the Four Values, Artificial Intelleligence, 102(1), 1998, 97-141.
- [6] Banerjee, M.: Rough sets and three-valued Łukasiewicz logic, Fundamenta Informaticae, 32, 1997, 213-220.
- [7] Belnap, N.: A useful four-valued logic, Modern Uses of Many Valued Logic (G. Eptein, J. Dunn, Eds.), Reidel, 1977, 8-37.
- [8] Bolc, L., Borowik, P.: Many-Valued Logics, 1. Theoretical Foundations, Springer, Berlin, 1992.
- [9] Damásio, C. V., Pereira, L.: A survey of paraconsistent semantics for logic programs, Handbook of Defeasible Reasoning and Uncertainty Management Systems (D. M. Gabbay, P. Smets, Eds.), vol. 2, Kluwer Academic Publishers, 1998, 241-320.
- [10] Doherty, P., Łukaszewicz,W., Skowron, A., Szałas, A.: Knowledge Representation Techniques. A Rough Set Approach, vol. 202 of Studies in Fuziness and Soft Computing, Springer-Verlag, 2006.
- [11] Doherty, P., Łukaszewicz, W., Szałas, A.: Tolerance Spaces and Approximative Representational Structures, Proc. 26th German Conf. on AI, KI'2003 (A. Günter, R. Kruse, B. Neumann, Eds.), LNAI, vol. 2821 of LNAI, Springer-Verlag, 2003, 475-489.
- [12] Doherty, P., Łukaszewicz, W., Szałas, A.: Communication between Agents with Heterogeneous Perceptual Capabilities, Journal of Information Fusion, 8(1), 2007, 56-69.
- [13] Doherty, P., Szałas, A.: On the Correspondence between Approximations and Similarity, Proceedings of 4th International Conference on Rough Sets and Current Trends in Computing, RSCTC'2004 (S. Tsumoto, R. Slowinski, J. Komorowski, J. Grzymala-Busse, Eds.), LNAI, vol. 3066 of LNAI, Springer-Verlag, 2004, 143-152.
- [14] Doherty, P., Szałas, A.: A Correspondence Framework between Three-valued Logics and Similarity-based Approximate Reasoning, Fundamenta Informaticae, 75(1-4), 2007.
- [15] Dubois, D., Prade, H.: Putting Rough Sets and Fuzzy Sets Together, Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, Kluwer, 1992, 203-232.
- [16] Fitting, M.: Fixpoint semantics for logic programming. A survey, Theoretical Computer Science, 278(1-2), 2002, 25-51.
- [17] Fitting, M. C.: Bilattices in Logic Programming, 20th International Symposium on Multiple-Valued Logic (G. Epstein, Ed.), IEEE CS Press, Los Alamitos, 1990, 238-247.
- [18] Ginsberg, M.: Multivalued logics: a uniform approach to reasoning in AI, Computational Intelligence, 4, 1988, 256-316.
- [19] Grabowski, A.: Basic Properties of Rough Sets and Rough Membership Function, Formalized Mathematics, 12(1), 2004.
- [20] Knaster, B.: Un theoreme sur les fonctions d'ensembles, Ann. Soc. Polon. Math., 6, 1928, 133-134.
- [21] Małuszyński, J., Szałas, A., Vitória, A.: A Four-Valued Logic for Rough Set-like Approximate Reasoning, Transactions on Rough Sets, Commemorative Issue (I. Duntsch, J. Grzymala-Busse, E. Orlowska, L. Polkowski, Eds.), LNCS, vol. 4374 of LNCS, 2007, 176-190.
- [22] Małuszyński, J., Szałas, A., Vitória, A.: Paraconsistent Logic Programs with Four-valued Rough Sets, Proceedings of 6th International Conference on Rough Sets and Current Trends in Computing (RSCTC 2008) (C.-C. Chan, J. Grzymala-Busse,W. Ziarko, Eds.), LNAI, vol. 5306 of LNAI, 2008, 41-51.
- [23] Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.
- [24] Radzikowska, A. M., Kerre, E. E.: A comparative study of fuzzy rough sets, Fuzzy Sets and Systems, 126, 2002, 137-155.
- [25] Rescher, N.: Many-Valued Logic, McGraw Hill, New York, 1969.
- [26] Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces, Fundamenta Informaticae, 27, 1996, 245-253.
- [27] Słowiński, R., Vanderpooten,D.: A generalized definition of rough approximations based on similarity, IEEE Trans. on Data and Knowledge Engineering, 12(2), 2000, 331-336.
- [28] Sunderraman, R., Wang, H.: Paraconsistent Intuitionistic Fuzzy Relational Data Model, 2004, Http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0410054.
- [29] Tarski, A.: A Lattice-theoretical Fixpoint Theorem and its Applications, Pacific Journal of Mathematics, 5(2), 1965, 285-309.
- [30] Vitória, A.: A Framework for Reasoning with Rough Sets., Transactions on Rough Sets IV, 3700, 2005, 178-276.
- [31] Vitória, A.: Rule Languages for Rough Sets, University of Linköping, 2010, Ph.D. Thesis, in preparation.
- [32] Vitória, A., Szałas, A., Małuszyński, J.: A Four-Valued Extension of Rough Sets, Proceedings of Rough Sets and Knowledge Technology (RSKT 2008) (G.Wang, T. Li, J. Grzymala-Busse, D. Miao, A. Skowron, Y. Yao, Eds.), LNAI, vol. 5009 of LNAI, 2008, 106-114.
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0008-0080