Production systems with negation as failure

We study action rule-based systems with two forms of negation, namely classical negation and "negation as failure to find a course of actions." We show by several examples that adding negation as failure to such systems increases their expressiveness in the sense that real life problems can be represented in a natural and simple way. Then, we address the problem of providing a formal declarative semantics to these extended systems by adopting an argumentation-based approach which has been shown to be a simple unifying framework for understanding the declarative semantics of various nonmonotonic formalisms. In this way, we naturally define the grounded (well-founded), stable, and preferred semantics for production systems with negation as failure. Next, we characterize the class of stratified production systems, which enjoy the properties that the above mentioned semantics coincide and that negation as failure to find a course of actions can be computed by a simple bottom-up operator. Stratified production systems can be implemented on top of conventional production systems in two ways. The first way corresponds to the understanding of stratification as a form of priority assignment between rules. We show that this implementation, though sound, is not complete in the general case. Hence, we propose a second implementation by means of an algorithm which transforms a finite stratified production system into a classical one. This is a sound and complete implementation, though computationally hard, as shown in the paper.