Abstract
We present algebraic formalisms for different kinds of information systems, viz. deterministic, incomplete, and non-deterministic. Algebraic structures generated from these information systems are considered and corresponding abstract algebras are proposed. Representation theorems for these classes of abstract algebras are proved, which lead us to equational logics for deterministic, incomplete, and non-deterministic information systems.
A part of this chapter appeared in preliminary form in the proceedings of the conference PReMI 2011.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Balbiani, P.: Axiomatization of logics based on Kripke models with relative accessibility relations. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 553–578. Physica Verlag, Heidelberg (1998)
Balbiani, P., Orłowska, E.: A hierarchy of modal logics with relative accessibility relations. Journal of Applied Non-Classical Logics 9(2-3), 303–328 (1999)
Balbiani, P., Vakarelov, D.: A modal logic for indiscernibility and complementarity in information systems. Fundamenta Informaticae 50, 243–263 (1950)
Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neuro Computing: Techniques for Computing with Words, pp. 157–184. Springer, Berlin (2004)
Banerjee, M., Khan, M. A.: Propositional Logics from Rough Set Theory. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI, Part I. LNCS, vol. 4374, pp. 1–25. Springer, Heidelberg (2007)
Birkhoff, G.: On the structure of abstract algebras. Proceedings of the Cambridge Philosophical Society 29, 441–464 (1935)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Comer, S.: An algebraic approach to the approximation of information. Fundamenta Informaticae XIV, 492–502 (1991)
Düntsch, I., Gediga, G., Orłowska, E.: Relational attribute systems. International Journal of Human Computer Studies 55(3), 293–309 (2001)
Düntsch, I., Gediga, G., Orłowska, E.: Relational Attribute Systems II: Reasoning with Relations in Information Structures. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII, Part II. LNCS, vol. 4400, pp. 16–35. Springer, Heidelberg (2007)
Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. Springer, Heidelberg (2002)
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–200 (1990)
Henkin, L., Monk, J.D., Tarski, A.: Cylindric Algebras, Part I. North-Holland Pub. Co., Amsterdam (1971)
Iwiński, T.B.: Algebraic approach to rough sets. Bulletin of the Polish Academy of Sciences (Math) 35(9-10), 673–683 (1987)
Khan, M. A., Banerjee, M.: A Logic for Complete Information Systems. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS(LNAI), vol. 5590, pp. 829–840. Springer, Heidelberg (2009)
Khan, M.A., Banerjee, M.: Logics for information systems and their dynamic extensions. ACM Transactions on Computational Logic 12(4), 29 (2011)
Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in Decision-Making, pp. 3–98. Springer, Singapore (1999)
Konikowska, B.: A formal language for reasoning about indiscernibility. Bulletin of the Polish Academy of Sciences 35, 239–249 (1987)
Konikowska, B.: A logic for reasoning about relative similarity. Studia Logica 58, 185–226 (1997)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. Information Sciences 112, 39–49 (1998)
Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113, 271–292 (1999)
Lin, T.Y., Yao, Y.Y.: Neighborhoods system: measure, probability and belief functions. In: Tsumoto, S., Kobayashi, S., Yokomori, T., Tanaka, H., Nakamura, A. (eds.) Proceedings of the The Fourth International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, November 6-8, pp. 202–207. The University of Tokyo, Tokyo (1996)
Orłowska, E.: Dynamic information system. Fundamenta Informaticae 5, 101–118 (1982)
Orłowska, E.: Logic of Indiscernibility Relations. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 177–186. Springer, Heidelberg (1985)
Orłowska, E.: Logic of nondeterministic information. Studia Logica 1, 91–100 (1985)
Orłowska, E.: Kripke semantics for knowledge representation logics. Studia Logica XLIX, 255–272 (1990)
Orłowska, E.: Rough set semantics for non-classical logics. In: Ziarko, W. (ed.) Rough Sets,Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Workshops in Computing, Banff, Alberta, Canada, October 12-15, pp. 143–148. Springer, Heidelberg (1993)
Orłowska, E., Pawlak, Z.: Representation of nondeterministic information. Theoretical Computer Science 29, 27–39 (1984)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11(5), 341–356 (1982)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Polkowski, L.: Rough Sets: Mathematical Foundations. Physica-Verlag, Heidelberg (2002)
Pomykała, J.A.: Approximation, similarity and rough constructions. ILLC prepublication series for computation and complexity theory CT-93-07, University of Amsderdam (1993)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)
Ślęzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Vakarelov, D.: Abstract characterization of some knowledge representation systems and the logic NIL of nondeterministic information. In: Jorrand, P., Sgurev, V. (eds.) Artificial Intelligence II, pp. 255–260. North–Holland (1987)
Vakarelov, D.: Modal logics for knowledge representation systems. Theoretical Computer Science 90, 433–456 (1991)
Wasilewski, L., Ślęzak, D.: Foundations of rough sets from vagueness perspective. In: Hassanien, A.E., Suraj, Z., Ślęzak, D., Lingras, P. (eds.) Rough Computing, Theories, Technologies and Applications, pp. 1–37. IGI Global, Hershey (2008)
Yao, Y.Y.: Generalized rough set models. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 286–318. Physica-Verlag, Heidelberg (1998)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Khan, M.A., Banerjee, M. (2013). Algebras for Information Systems. In: Skowron, A., Suraj, Z. (eds) Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam. Intelligent Systems Reference Library, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30344-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-30344-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30343-2
Online ISBN: 978-3-642-30344-9
eBook Packages: EngineeringEngineering (R0)