Integrating Model Theoretic and Proof Theoretic Interpretation of Logic Programs

Abstract

We present an Interpretation algorithm for pure logic programs, in the sense of a many-sorted Horn logic, which combines both model and proof theoretic evaluation of goals. While proof theoretic goal evaluation is the Standard deductive mechanism of proving a goal from a set of Horn clauses, the model theoretic aspect goes back to searching a model for a Solution of the given goal. Since modeis of logic programs tend to be infinite and we want to store our modeis in a relational database, we can consider only finite excerpts of modeis, called views in our discussion. The idea of the integrated truth checking algorithm is to solve a goal by first Consulting the database for a possible Solution and to initiate a deduction process in case no such immediate Solutions can be found. We prove that this evaluation strategy is correct but — in general — not complete.