Hybridizing concept languages

Abstract

This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the welldknown 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 firstdorder 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 TBoxd and ABoxdstatements. Subsequent addition of the universal modality allows the notion of subsumption to be internalized, and enables the representation of queries to arbitrary firstdorder knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention to a littledknown body of work by the late Arthur Prior.