Equivalence and Minimization of Conjunctive Queries Under Combined Semantics (extended abstract)

The problems of query containment, equivalence, and minimization are fundamental problems in the context of query processing and optimization. In their classic work [2] published in 1977, Chandra and Merlin solved the three problems for the language of conjunctive queries (CQ queries) on relational data, under the “set-semantics ” assumption for query evaluation. While the results of [2] have been very influential in database research, it was recognized long ago that the set semantics does not correspond to the semantics of the standard commercial query language SQL. Alternative semantics, called bag and bag-set semantics, have been studied since 1993; Chaudhuri and Vardi in [5] outlined necessary and sufficient conditions for equivalence of CQ queries under these semantics. (The problems of containmen