Hybridizing concept languages

This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the well-known correspondences between modal and description logics, two hybrid languages are defined. These languages are called `hybrid' because, as well as the familiar propositional variables and modal operators, they also contain variables across individuals and a binder that binds these variables. As is shown, combining aspects of modal and first-order logic in this manner allows the expressivity of concept languages to be boosted in a natural way, making it possible to define number restrictions, collections of individuals, irreflexivity of roles, and TBox- and ABox-statements. Subsequent addition of the universal modality allows the notion of subsumption to be internalized, and enables the representation of queries to arbitrary first-order knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention to a little-known body of work by the late Arthur Prior.