2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2017)

Reykjavik, Iceland

June 20, 2017 to June 23, 2017

ISBN: 978-1-5090-3019-4

pp: 1-10

Dimitri Surinx , Hasselt University, Belgium

Jan Van den Bussche , Hasselt University, Belgium

Dirk Van Gucht , Indiana University, USA

ABSTRACT

The algebra of binary relations provides union and composition as basic operators, with the empty set as neutral element for union and the identity relation as neutral element for composition. The basic algebra can be enriched with additional features. We consider the diversity relation, the full relation, intersection, set difference, projection, coprojection, converse, and transitive closure. It is customary to express boolean queries on binary relational structures as finite conjunctions of containments. We investigate which features are primitive in this setting, in the sense that omitting the feature would allow strictly less boolean queries to be expressible. Our main result is that, modulo a finite list of elementary interdependencies among the features, every feature is indeed primitive.

INDEX TERMS

Algebra, Database languages, Testing, Semantics, Query processing, Vocabulary

CITATION

Dimitri Surinx,
Jan Van den Bussche,
Dirk Van Gucht,
"The primitivity of operators in the algebra of binary relations under conjunctions of containments",

*2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)*, vol. 00, no. , pp. 1-10, 2017, doi:10.1109/LICS.2017.8005122