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 Π_p2-complete, and NP-complete in some restricted cases.