Solving the Projection Problem with OWL2 Reasoners: Experimental Study

We evaluate HERMIT, an OWL2 reasoner, on a set of test cases that emerge from an unusual but very practical way of using Description Logics (DLs). In the field of reasoning about actions, the projection problem is an elemental problem that deals with answering whether a certain formula holds after doing a sequence of actions starting from some initial states represented using an incomplete theory. We consider a fragment of the situation calculus and Reiter’s basic action theories (BAT) such that the projection problem can be reduced to the satisfiability problem in an expressive description logic ALCO . We adapt an approach called regression where an input query is equivalently transformed until it can be directly checked against the initial theory supplemented with the unique name axioms (UNA) without any consideration to the rest of the BAT. To study regression in practice, we implemented it in C++, defined an XML SCHEMA to describe a BAT and queries, created 7 domains some of which are inspired from well-known planning competition domains, and invented generators that can create random but meaningful instances of the projection problem. The formula resulting from regressing a projection query, together with the initial theory and UNA, is fed to an OWL2 reasoner to answer whether the regressed query holds given the initial theory and UNA. We measure the input formula using a number of metrics, such as a number of U-role occurrences and a number of individuals, and evaluate the performance of HERMIT on formulas along each