Abstract
We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd’s model of data in which we consider ordinal ranks of tuples in data tables expressing degrees to which tuples match queries. In this setting, we show that ranks assigned to tuples are insensitive to small changes, i.e., small changes in the input data do not yield large changes in the results of queries.
Supported by grant no. P103/11/1456 of the Czech Science Foundation and internal grant of Palacky University no. PrF_2012_029. DAMOL is supported by project reg. no. CZ.1.07/2.3.00/20.0059 of the European Social Fund in the Czech Republic.
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References
Abiteboul, S., et al.: The lowell database research self-assessment. Commun. ACM 48(5), 111–118 (2005)
Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)
Belohlavek, R., Vychodil, V.: Logical foundations for similarity-based databases. In: Chen, L., Liu, C., Liu, Q., Deng, K. (eds.) DASFAA 2009 Workshops. 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: Proceedings of the ACM SAC 2010, pp. 1648–1655. ACM Press (2010)
Belohlavek, R., Vychodil, V.: Codd’s relational model from the point of view of fuzzy logic. J. Logic and Comput. 21(5), 851–862 (2011)
Birkhoff, G.: Lattice theory. American Mathematical Society, Providence (1940)
Buckles, B.P., Petry, F.E.: Fuzzy databases in the new era. In: Proceedings of the ACM SAC 1995, Nashville, TN, pp. 497–502. ACM Press (1995)
Cavallo, R., Pittarelli, M.: The theory of probabilistic databases. VLDB 1987, 71–81 (1987)
Codd, E.F.: A Relational Model of Data for Large Shared Data Banks. Commun. ACM 13(6), 377–387 (1970)
Dalvi, N., Ré, C., Suciu, D.: Probabilistic databases: diamonds in the dirt. Commun. ACM 52, 86–94 (2009)
Dalvi, N., Suciu, D.: Efficient query evaluation on probabilistic databases. VLDB J. 16, 523–544 (2007)
Dalvi, N., Suciu, D.: Management of probabilistic data: foundations and challenges. In: ACM PODS 2007, pp. 1–12 (2007)
Date, C.J.: Database Relational Model: A Retrospective Review and Analysis. Addison Wesley, Reading (2000)
Date, C.J., Darwen, H.: Databases, Types and the Relational Model, 3rd edn. Addison Wesley, Reading (2006)
Fagin, R.: Combining fuzzy information: an overview. ACM SIGMOD Record 31(2), 109–118 (2002)
Gerla, G.: Fuzzy Logic. Mathematical Tools for Approximate Reasoning. Kluwer, Dordrecht (2001)
Goguen, J.A.: The logic of inexact concepts. Synthese 18, 325–373 (1968-1969)
Gottwald, S.: Mathematical fuzzy logics. Bull. for Symbolic Logic 14(2), 210–239 (2008)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Hájek, P.: On very true. Fuzzy Sets Syst. 124, 329–333 (2001)
Illyas, I.F., Aref, W.G., Elmagarmid, A.K.: Supporting top-\(k\) join queries in relational databases. VLDB J. 13, 207–221 (2004)
Imieliński, T., Lipski, W.: Incomplete information in relational databases. J. ACM 31, 761–791 (1984)
Koch, C.: On query algebras for probabilistic databases. SIGMOD Record 37(4), 78–85 (2008)
Li, C., Chang, K.C.-C., Ilyas, I.F., Song S.: RankSQL: Query Algebra and Optimization for Relational top-k queries. In: ACM SIGMOD 2005, pp. 131–142. ACM Press (2005)
Maier, D.: The Theory of Relational Databases. Comp. Sci. Press, Rockville (1983)
Olteanu, D., Huangm, J., Koch, C.: Approximate confidence computation in probabilistic databases. IEEE ICDE 2010, 145–156 (2010)
Pavelka, J.: On fuzzy logic I, II, III. Z. Math. Logik Grundlagen Math. 25, 45–52; 25, 119–134; 25, 447–464 (1979)
Raju, K.V.S.V.N., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Trans. Database Systems 13(2), 129–166 (1988)
Shenoi, S., Melton, A.: Proximity relations in the fuzzy relational database model. Fuzzy Sets Syst. 100, 51–62 (1999)
Suciu, D., Olteanu, D., Ré, C., Koch, C.: Probabilistic Databases. Synthesis Lectures on Data Management. Morgan & Claypool Publishers (2011)
Takahashi, Y.: Fuzzy database query languages and their relational completeness theorem. IEEE Trans. Knowl. Data Eng. 5, 122–125 (1993)
Takeuti, G., Titani, S.: Globalization of intuitionistic set theory. Ann. Pure Appl. Logic 33, 195–211 (1987)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
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Belohlavek, R., Urbanova, L., Vychodil, V. (2013). Sensitivity Analysis for Declarative Relational Query Languages with Ordinal Ranks. In: Tompits, H., et al. Applications of Declarative Programming and Knowledge Management. INAP WLP 2011 2011. Lecture Notes in Computer Science(), vol 7773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41524-1_4
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