Equivalence of queries that are sensitive to multiplicities

Sara Cohen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The query equivalence problem has been studied extensively for set-semantics and, more recently, for bag and bag-set semantics. However, SQL queries often combine set, bag and bag-set semantics. For example, an SQL query that returns a multiset of elements may call a subquery or view that returns a set of elements. Queries may access both relations that do not contain duplicates, as well as relations with duplicates. As another example, in SQL one can compute a multiset-union of queries, each of which returns a set of answers. This paper presents combined semantics, which formally models query evaluation combining set, bag and bag-set semantics. The equivalence problem for queries evaluated under combined semantics is studied. A sufficient condition for equivalence is presented. For several important common classes of queries necessary and sufficient conditions for equivalence are presented.

Original languageAmerican English
Pages (from-to)765-785
Number of pages21
JournalVLDB Journal
Issue number3
StatePublished - Jun 2009

Bibliographical note

Funding Information:
An early version of this article appeared in [7]. This paper extends [7] to include bag semantics, in addition to set and bag-set semantics. This work was partially supported by the Israel Science Foundation (Grant 1032/05).


  • Bag semantics
  • Combined semantics
  • Datalog
  • Query equivalence
  • Set semantics


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