A Note on Concepts and Distances

We combine the description logic ALC with the metric logics defined Entities that are conceived of as abstract points in the realm of ALC are given a spatial extension via an `extension relation,' connecting 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.

• Type: Conference
• Year: 2001
• Where: DLOG
• Authors: Oliver Kutz, Frank Wolter, Michael Zakharyaschev
• Keywords: Automated Reasoning, Description Logic Alc, DLOG 2001, Extension Relation, Metric Space