On the Undecidability of the Situation Calculus Extended with Description Logic Ontologies

In this paper we investigate situation calculus action theories extended with ontologies, expressed as description logics TBoxes that act as state constraints. We show that this combination, while natural and desirable, is particularly problematic: it leads to undecidability of the simplest form of reasoning, namely satisfiability, even for the simplest kinds of description logics and the simplest kind of situation calculus action theories.