A representation theorem for quantales

AbstractWe define a relational quantale to be a quantale whose elements are relations on a set A, ordered by inclusion and forming a monoid under relational composition. Such quantales have been studied in several areas of theoretical computer science, and constitute a sound and complete class of models for non-commutative linear logic. We show that every quantale is isomorphic to a relational quantale, and investigate the classification of quantales according to properties of their representations as relational quantales