Reasoning with prototypes in the description logic ALC using weighted tree automata

Abstract

We introduce an extension to Description Logics that allows us to use prototypes to define concepts. To accomplish this, we introduce the notion of prototype distance functions (pdfs), which assign to each element of an interpretation a distance value. Based on this, we define a new concept constructor of the form P~n(d) for ∼ ∈ {, ≥}, which is interpreted as the set of all elements with a distance ∼ n according to the pdf d. We show how weighted alternating parity tree automata (wapta) over the non-negative integers can be used to define pdfs, and how this allows us to use both concepts and pointed interpretations as prototypes. Finally, we investigate the complexity of reasoning in ALCP(wapta), which extends the Description Logic ALC with the constructors P~n(d) for pdfs defined using wapta.