Computing Uniform Interpolants of ALCH-Ontologies with Background Knowledge

ABSTRACT. Uniform interpolation is a technique to restrict the concept and roles symbols used in an ontology to a specified subset, while preserving all logical entailments that can be expressed using that subset. We propose the notion of relative uniform interpolation, where knowledge from a second ontology is taken into account, and present a method for the description logic ALCH. Relative uniform interpolation of ontologies corresponds to strongest necessary conditions of formulae studied in classical logics.