Prolog Technology for Default Reasoning: Proof Theory and Compilation Techniques

The aim of this work is to show how Prolog technology can he used for efficient implementation of query answering in default logics. The idea is to translate a default theory along with a query into a Prolog program and a Prolog query such that the original query is derivable from the default theory iff the Prolog query is derivable from the Prolog program. In order to comply with the goal-oriented proof search of this approach, we focus on default theories supporting local proof procedures, as exemplified by so-called semi-monotonic default theories. Although this does not capture general default theories under Reiter’s interpretation, it does so under alternative ones’. For providing theoretical underpinnings, we found the resulting compilation techniques upon a top-down proof procedure based on model elimination. We show how the notion of a model elimination proof can be refined to capture default proofs and how standard techniques for implementing and improving model elimination theorem provers (regularity, lemmas) can be adapted and extended to default reasoning. This integrated approach allows us to push the concepts needed for handling defaults from the underlying calculus onto the resulting compilation techniques. This meth’od for default theorem proving is complemented by a model-based approach to incremental consistency checking. We show that the crucial task of consistency checking can benefit from keeping models in order to restrict the attention to ultimately necessary consistency checks. This is supported by the concept of default lemmas that allow for an additional avoidance of redundancy.