A Note on Concepts and Distances.
Oliver Kutz, Frank Wolter, and Michael Zakharyaschev
We combine the description logic ALC with the metric logics defined in "Semi-qualitative reasoning about distances" (Sturm et al. 2000}. Entities that are conceived of as abstract points in the realm of ALC are given a spatial extension via an `extension relation,' connecting abstract points in the domain of an ALC-model to points in a metric space. Conversely, regions in the metric space are connected via the converse `extension relation' to certain points in the ALC-model. We prove the decidability of the satisfiability problem for the resulting hybrid formalism, give a few examples, and discuss further extensions of the ideas introduced.