Foundations for Uniform Interpolation and Forgetting in Expressive Description Logics

We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform interpolants and their existence in terms of bisimulations, tight complexity bounds for deciding the existence of uniform interpolants, an approach to computing interpolants when they exist, and tight bounds on their size. We use a mix of modeltheoretic and automata-theoretic methods that, as a by-product, also provides characterizations of and decision procedures for conservative extensions.