A Monotone Preservation Result for Boolean Queries Expressed as a Containment of Conjunctive Queries

Abstract: When a relational database is queried, the result is normally a relation. Some queries, however, only require a yes/no answer; such queries are often called boolean queries. It is customary in database theory to express boolean queries by testing nonemptiness of query expressions. Another interesting way for expressing boolean queries are containment statements of the form $Q_1 \subseteq Q_2$ where $Q_1$ and $Q_2$ are query expressions. Here, for any input instance $I$, the boolean query result is $\mathit{true}$ if $Q_1(I)$ is a subset of $Q_2(I)$ and $\mathit{false}$ otherwise. In the present paper we will focus on nonemptiness and containment statements about conjunctive queries. The main goal is to investigate the monotone fragment of the containments of conjunctive queries. In particular, we show a preservation like result for this monotone fragment. That is, we show that, in expressive power, the monotone containments of conjunctive queries are exactly equal to conjunctive queries under nonemptiness.