Construction of Belief Sets for Logic Programs and Default Theories

We present a uniied approach to the construction of belief sets for logic programs with the classical connective of negation, disjunctive logic programs, and what we call arbitrary logic programs that contain an arbitrary formula in the head and arbitrary formulas in the premises of a program rule. The approach is based on a nondetermin-istic iterative operator constrained by a dynamic preference relation, which is drawn automatically during the iterative process. This iterative construction can be viewed as an inference-based extension to the stable model semantics in that every stable model with a well-founded preference relation is computed as an iterative answer set. For function-free datalog programs, the construction itself suggests a sound and complete proof procedure, and there exists a polynomial time algorithm for computing an iterative answer set. We compare this method with Brewka's method of determining priority preserving extensions and show that the formulation of arbitrary logic programming provides a desirable formalism for default reasoning.