Relational Computation of Sets of Relations

Abstract

We present a technique for the relational computation of sets $\mathcal {R}$ of relations. It is based on a specification of a relation R to belong to $\mathcal {R}$ by means of an inclusion $\mathfrak {s}\,\subseteq \,\mathfrak {t}$, where $\mathfrak {s}$ and $\mathfrak {t}$ are relation-algebraic expressions constructed from a vector model of R in a specific way. To get the inclusion, we apply properties of a mapping that transforms relations into their vectors models and, if necessary, point-wise reasoning. The desired computation of $\mathcal {R}$ via a relation-algebraic expression $\mathfrak {r}$ is then immediately obtained from $\mathfrak {s}\,\subseteq \,\mathfrak {t}$ using a result of [3]. Compared with a direct development of $\mathfrak {r}$ from a logical specification of R to belong to $\mathcal {R}$, the proposed technique is much more simple. We demonstrate its use by some classes of specific relations and also show some applications.