A Note on Concepts and Distances.
Oliver Kutz, Frank Wolter, Michael Zakharyaschev · BIROn (Birkbeck, University of London) · 2001
We combine the description logic ALC with the metric logics defined in [15]. 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. 1