Query containment under bag and bag-set semantics

Abstract

Conjunctive queries (CQs) are at the core of query languages encountered in many logic-based research fields such as AI, or database systems. The majority of existing work assumes set semantics but often in real applications the manipulation of duplicate tuples is required. One of the major problems that arises as part of advanced features of query optimization, data integration, query reformulation and many other research topics is testing for containment of such queries. In this work, we investigate the complexity of query containment problem for CQs under bag semantics (i.e. duplicate tuples are allowed in both the database and the results of queries) and under bag-set semantics (i.e. duplicates are allowed in the result of the queries but not in the database). We derive complexity results for these problems for five major subclasses of CQs; and we also find necessary conditions for CQ query containment. The general case of these problems remains open.