Abstract
We study conjunctive queries that combine information from multiple sources. The need for combining information is manifest for instance in multimedia systems. It has recently been recognized that query semantics for these systems should be based on some quantitative model, such as fuzzy logic. Further complications arise, however, since the semantics used internally by subsystems, and the semantics used externally to combine information, are not necessarily the same.
In this paper we give a solution based on general multivalued logics with lattice-based semantics. The internal and external semantics are tied to each other through the concept of a bilattice. Queries using both internal level and external level conjunctions have a natural semantics in bilattices. We then show that homomorphism techniques from core database theory carry over to query containment for internal/external conjunctive queries in the bilattice-setting. We also show that the computational complexity of determining containment of internal/external conjunctive queries is in general Π 2p -complete, and NP-complete in some restricted cases.
Research conducted while the first author was visiting at Université de Paris-Sud, Laboratoire de Recherche en Informatique.
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References
Abiteboul S., Hull R., and Vianu V. Foundations of Databases. Addison-Wesley, Reading Ma. 1995.
Belnap N. D., Jr. A useful four-valued logic. In: J. Michael Dunn and G. Epstein (Eds.), Modern Uses of Multiple-Valued Logic, Reidel, 1977, pp. 89–148.
Chandra A. K. and Merlin P. M. Optimal implementation of conjunctive queries in relational databases. Proc. 9th Annual ACM Symp. on the Theory of Computing, pp. 77–90.
Chaudhuri S. and Vardi M. Optimization of real conjunctive queries. Proc. 12th ACM Symp. on Principles of Database Systems, pp. 59–70.
Fagin R. Combining fuzzy information from multiple systems. Proc. 15th ACM Symp. on Principles of Database Systems.
Fitting M. Bilattices and the semantics of logic programming. J. Logic Programming 11, 91–116.
Fitting M. The family of stable models. J. Logic Programming 17, 197–225.
Ginsberg M. L. Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, pp. 265–316.
Ioannidis Y. E. and Ramakrishnan R. Containment of conjunctive queries: beyond relations as sets. ACM Transactions on Database Systems 20:3, pp. 288–324.
Sagiv Y. and Yannakakis M. Equivalences among relational expressions with the union and difference operators. J. ACM 27:4, pp. 633–655.
Stockmeyer L. J. The polynomial-time hierarchy. Theoret. Comput. Sci. 3, pp. 1–22.
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© 1996 Springer-Verlag Berlin Heidelberg
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Grahne, G., Spyratos, N., Stamate, D. (1996). Semantics and containment of queries with internal and external conjunctions. In: Afrati, F., Kolaitis, P. (eds) Database Theory — ICDT '97. ICDT 1997. Lecture Notes in Computer Science, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62222-5_37
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DOI: https://doi.org/10.1007/3-540-62222-5_37
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