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.
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