Category-based Semantic Paramodulation

We introduce the concept of semantic paramodulation as a \semantic" de nition of paramodulation (in the sense that it applies to any model, not only to the term algebra) within the framework of category-based equational logic (introduced by [8, 9]). This not only generalises the traditional syntactic approaches to paramodulation, but also provides an abstract framework for a uni ed treatment of paramodulation and its re nements in a wide class of equational logical systems. This includes many sorted algebra, order sorted algebra, rewrite models, Horn clause logic, equational logic modulo axioms, constraint logic, and any combination of these. The possibility to give a direct treatment of refutations modulo axioms and to constraint computations is of special importance. Moreover, semantic paramodulation gives the possibility to develop equational logic programming over non-conventional structures (such as graphs) whose models might be essentially di erent from the traditional set-theoretic ones. We lay bare the architecture of the completeness of paramodulation. The study of the paramodulation relation induced by a program on a model lies at the core of a general scheme for proving the completeness of paramodulation-based operational semantics that we propose in this paper.