Bottom-up computation of the Fitting model for general deductive databases

摘要

General logic programs are those that contain both positive and negative subgoals in their clause bodies. For such programs Fitting proposed an elegant 3-valued minimum model semantics that avoids some impracticalities of previous approaches. Here we present a method to compute this Fitting model for deductive databases. We introducepartial relations, which are the semantic objects associated with predicate symbols, and define algebraic operators over them. The first step in our model computation method is to convert the database rules into partial relation definitions involving these operators. The second step is to build the minimum model iteratively. We give algorithms for both steps and show their termination and correctness. We also suggest extensions to our method for computing the well-founded model proposed by van Gelder, Ross and Schlipf.