Uniform Interpolation of $\mathcal{ALC}$ -Ontologies Using Fixpoints
Identifieur interne : 001456 ( Main/Exploration ); précédent : 001455; suivant : 001457Uniform Interpolation of $\mathcal{ALC}$ -Ontologies Using Fixpoints
Auteurs : Patrick Koopmann [Royaume-Uni] ; Renate A. Schmidt [Royaume-Uni]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We present a method to compute uniform interpolants with fixpoints for ontologies specified in the description logic $\mathcal{ALC}$ . The aim of uniform interpolation is to reformulate an ontology such that it only uses a specified set of symbols, while preserving consequences that involve these symbols. It is known that in $\mathcal{ALC}$ uniform interpolants cannot always be finitely represented. Our method computes uniform interpolants for the target language $\mathcal{ALC}\mu$ , which is $\mathcal{ALC}$ enriched with fixpoint operators, and always computes a finite representation. If the result does not involve fixpoint operators, it is the uniform interpolant in $\mathcal{ALC}$ . The method focuses on eliminating concept symbols and combines resolution-based reasoning with an approach known from the area of second-order quantifier elimination to introduce fixpoint operators when needed. If fixpoint operators are not desired, it is possible to approximate the interpolant.
Url:
DOI: 10.1007/978-3-642-40885-4_7
Affiliations:
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