Abstract
We show a complete axiomatization of a logic of attribute implications describing dependencies between attributes of objects which are observed in consecutive points in time. The attribute implications we consider are if-then formulas expressing presence of attributes of objects relatively in time. The semantics of the attribute implications is defined based on presence/absence of attributes of objects in consecutive points of time. The presented results extend the classic results on Armstrong-style completeness of the logic of attribute implications by using the time points as additional component. The ordinary results can be seen as special case of our results when only a single time point is considered.
Supported by grant no. P202/14–11585S of the Czech Science Foundation.
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References
Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data, SIGMOD 1993, pp. 207–216. ACM, New York (1993)
Armstrong, W.W.: Dependency structures of data base relationships. In: Rosenfeld, J.L., Freeman, H. (eds.) Information Processing 1974: Proceedings of IFIP Congress, pp. 580–583. North Holland, Amsterdam (1974)
Bettini, C., Jajodia, S., Wang, X.S.: Time Granularities in Databases, Data Mining, and Temporal Reasoning. Springer (2000)
Cordero, P., Mora, A., de Guzmán, I.P., Enciso, M.: Non-deterministic ideal operators: An adequate tool for formalization in data bases. Discrete Applied Mathematics 156(6), 911–923 (2008)
Date, C.J., Darwen, H., Lorentzos, N.A.: Temporal Data and the Relational Model. Elsevier (2002)
Fagin, R.: Functional dependencies in a relational database and propositional logic. IBM Journal of Research and Development 21(6), 534–544 (1977)
Feng, L., Dillon, T., Liu, J.: Inter-transactional association rules for multi-dimensional contexts for prediction and their application to studying meterological data. Data Knowl. Eng. 37(1), 85–115 (2001)
Feng, L., Yu, J.X., Lu, H., Han, J.: A template model for multidimensional inter-transactional association rules. The VLDB Journal 11(2), 153–175 (2002)
Gabbay, D.M.: Tense systems with discrete moments of time, part I. Journal of Philosophical Logic 1(1), 35–44 (1972)
Gabbay, D.M.: Model theory for tense logics. Annals of Mathematical Logic 8(1-2), 185–236 (1975)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations, 1st edn. Springer-Verlag New York, Inc., Secaucus (1997)
Ganter, B., Obiedkov, S.: Implications in triadic formal contexts. In: Wolff, K.E., Pfeiffer, H.D., Delugach, H.S. (eds.) ICCS 2004. LNCS (LNAI), vol. 3127, pp. 186–195. Springer, Heidelberg (2004)
Guigues, J.L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)
Huang, Y.P., Kao, L.J., Sandnes, F.E.: Efficient mining of salinity and temperature association rules from argo data. Expert Syst. Appl. 35(1-2), 59–68 (2008)
Lee, A.J.T., Wang, C.S., Weng, W.Y., Chen, Y.A., Wu, H.W.: An efficient algorithm for mining closed inter-transaction itemsets. Data Knowl. Eng. 66(1), 68–91 (2008)
Lee, A.J.T., Wu, H.W., Lee, T.Y., Liu, Y.H., Chen, K.T.: Mining closed patterns in multi-sequence time-series databases. Data Knowl. Eng. 68(10), 1071–1090 (2009)
Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: Ellis, G., Rich, W., Levinson, R., Rich, W., Sowa, J.F. (eds.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)
Lloyd, J.W.: Foundations of Logic Programming. Springer-Verlag New York, Inc., New York (1984)
Lu, H., Feng, L., Han, J.: Beyond intratransaction association analysis: Mining multidimensional intertransaction association rules. ACM Trans. Inf. Syst. 18(4), 423–454 (2000)
Maier, D.: Theory of Relational Databases. Computer Science Pr., Rockville (1983)
Tung, A.K., Lu, H., Han, J., Feng, L.: Breaking the barrier of transactions: Mining inter-transaction association rules. In: Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 1999, pp. 297–301. ACM, New York (1999)
Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets. NATO Advanced Study Institutes Series, vol. 83, pp. 445–470. Springer, Netherlands (2009)
Zaki, M.J.: Mining non-redundant association rules. Data Mining and Knowledge Discovery 9, 223–248 (2004)
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Triska, J., Vychodil, V. (2014). Towards Armstrong-Style Inference System for Attribute Implications with Temporal Semantics. In: Torra, V., Narukawa, Y., Endo, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2014. Lecture Notes in Computer Science(), vol 8825. Springer, Cham. https://doi.org/10.1007/978-3-319-12054-6_8
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DOI: https://doi.org/10.1007/978-3-319-12054-6_8
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