Production Systems Need Negation as Failure

Phan Minh Dung, Paolo Mancarella

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 increase 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 can be computed by a simple bottom-up operator.

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