Abstract
We present a new axiomatization of logic for dependencies in data with grades, including ordinal data and data in an extension of Codd’s model that takes into account similarity relations on domains. The axiomatization makes possible an efficient method for automated reasoning for such dependencies that is presented in the paper. The presented method of automatic reasoning is based on a new simplification equivalence which allows to simplify sets of dependencies while retaining their semantic closures. We include two algorithms for computing closures and checking semantic entailment from sets of dependencies and present experimental comparison showing that the algorithms based on the new axiomatization outperform the algorithms proposed in the past.
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References
Aguilera, G., Cordero, P., Enciso, M., Mora, A., de Guzmán, I.P.: A Non-explosive Treatment of Functional Dependencies Using Rewriting Logic. In: Bazzan, A.L.C., Labidi, S. (eds.) SBIA 2004. LNCS (LNAI), vol. 3171, pp. 31–40. Springer, Heidelberg (2004)
Armstrong, W.: Dependency structures of data base relationships. In: IFIP Congress, pp. 580–583 (1974)
Beeri, C., Bernstein, P.A.: Computational problems related to the design of normal form relational schemas. ACM Trans. Database Syst. 4, 30–59 (1979)
Belohlavek, R., Vychodil, V.: Axiomatizations of fuzzy attribute logic. In: IICAI 2005, pp. 2178–2193 (2005)
Bělohlávek, R., Vychodil, V.: Attribute Implications in a Fuzzy Setting. In: Missaoui, R., Schmidt, J. (eds.) ICFCA 2006. LNCS (LNAI), vol. 3874, pp. 45–60. Springer, Heidelberg (2006)
Bělohlávek, R., Vychodil, V.: Data Tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases. In: Li Lee, M., Tan, K.-L., Wuwongse, V. (eds.) DASFAA 2006. LNCS, vol. 3882, pp. 644–658. Springer, Heidelberg (2006)
Belohlavek, R., Vychodil, V.: Properties of models of fuzzy attribute implications. In: SCIS & ISIS 2006, pp. 291–296 (2006)
Belohlavek, R., Vychodil, V.: Logical Foundations for Similarity-Based Databases. In: Chen, L., Liu, C., Liu, Q., Deng, K. (eds.) DASFAA 2009. LNCS, vol. 5667, pp. 137–151. Springer, Heidelberg (2009)
Belohlavek, R., Vychodil, V.: Query systems in similarity-based databases: logical foundations, expressive power, and completeness. In: ACM SAC, pp. 1648–1655 (2010)
Cordero, P., Enciso, M., Mora, A., de Guzmán, I.P.: SLFD logic: Elimination of data redundancy in knowledge representation. In: Garijo, F.J., Riquelme, J.-C., Toro, M. (eds.) IBERAMIA 2002. LNCS (LNAI), vol. 2527, pp. 141–150. Springer, Heidelberg (2002)
Fagin, R.: Combining fuzzy information: an overview. SIGMOD Record 31(2), 109–118 (2002)
Gerla, G.: Fuzzy Logic. Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht (2001)
Goguen, J.A.: The logic of inexact concepts. Synthese 19(3–4), 325–373 (1969)
Gottwald, S.: A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 98. Research Studies Press, Baldock (2000)
Gottwald, S.: Mathematical fuzzy logics. The Bulletin of Symbolic Logic 14(2), 210–244 (2008)
Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)
Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic: Studia Logica Library. Kluwer Academic Publishers, Dordrecht (1998)
Hájek, P.: On very true. Fuzzy Sets and Systems 124(3), 329–333 (2001)
Maier, D.: The theory of relational databases. Computer software engineering series. Computer Science Press (1983)
Mora, A., Aguilera, G., Enciso, M., Cordero, P., Perez de Guzman, I.: A new closure algorithm based in logic: SLFD-Closure versus classical closures. Inteligencia Artificial, Revista Iberoamericana de IA 10(31), 31–40 (2006)
Mora, A., Cordero, P., Enciso, M., Fortes, I., Aguilera, G.: Closure via functional dependence simplification. International Journal of Computer Mathematics 89(4), 510–526 (2012)
Pavelka, J.: On fuzzy logic I, II, III. Mathematical Logic Quarterly 25, 45–52 (1979)
Raju, K.V.S.V.N., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Transactions on Database Systems (TODS) 13, 129–166 (1988) ACM ID: 42344
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Belohlavek, R., Cordero, P., Enciso, M., Mora, A., Vychodil, V. (2012). An Efficient Reasoning Method for Dependencies over Similarity and Ordinal Data. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_36
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DOI: https://doi.org/10.1007/978-3-642-34620-0_36
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