Semantics and containment of queries with internal and external conjunctions
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 Πp2-complete, and NP-complete in some restricted cases.
Unable to display preview. Download preview PDF.
- [AHV95]Abiteboul S., Hull R., and Vianu V. Foundations of Databases. Addison-Wesley, Reading Ma. 1995.Google Scholar
- [Bel77]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.Google Scholar
- [CM77]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.Google Scholar
- [CV93]Chaudhuri S. and Vardi M. Optimization of real conjunctive queries. Proc. 12th ACM Symp. on Principles of Database Systems, pp. 59–70.Google Scholar
- [Fag96]Fagin R. Combining fuzzy information from multiple systems. Proc. 15th ACM Symp. on Principles of Database Systems.Google Scholar
- [Fit91]Fitting M. Bilattices and the semantics of logic programming. J. Logic Programming 11, 91–116.Google Scholar
- [Fit93]Fitting M. The family of stable models. J. Logic Programming 17, 197–225.Google Scholar
- [Gin88]Ginsberg M. L. Multivalued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, pp. 265–316.Google Scholar
- [IR95]Ioannidis Y. E. and Ramakrishnan R. Containment of conjunctive queries: beyond relations as sets. ACM Transactions on Database Systems 20:3, pp. 288–324.Google Scholar
- [SY80]Sagiv Y. and Yannakakis M. Equivalences among relational expressions with the union and difference operators. J. ACM 27:4, pp. 633–655.Google Scholar
- [Sto77]Stockmeyer L. J. The polynomial-time hierarchy. Theoret. Comput. Sci. 3, pp. 1–22.Google Scholar