Expanding logic programs

Abstract

We discuss the problem of finding acceptable models for (propositional) logic programs with negation and constraints.

It is well-known that although the well-founded semantics is defined for every general program, not every program with constraints has a wellfounded model. We will argue that, in case the program is consistent but has no well-founded model, we should look for an expansion of the current program having a well-founded model.

We will discuss some properties these expansions and the methods generating them should have. In particular we show that there are tractable and complete expansion methods, i.e., efficient methods returning an expansion having a well-founded model whenever the original program is consistent.

Furthermore, we will investigate the complexity of expansion minimization problems, showing that in general they are NP-hard. If, however, we restrict these problems to local minimization problems, they can be solved efficiently.

This work can be viewed as a logical reconstruction of ideas presented (procedurally) in truth-maintenance (e.g. dependency-directed backtracking), auto-epistemic logic and abductive reasoning.