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Abstract:
This paper shows how to increase the expressivity of concept languages
using a strategy called {\em hybridization}. Building on the
well-known correspondences between modal and description logics, two
{\em hybrid languages\/} are defined. These languages are called
`hybrid' because, as well as the familiar propositional variables and
modal operators, they also contain {\em variables across
individuals\/} and a binder that {\em 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 {\em 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.
