This paper presents an application of the concepts of siphons (deadlocks) and inhibitor arcs in Petri net theory to logic programs with negations. More specifically, an extended Petri net is used to model function-free normal logic programs. In this model, because of the presence of inhibitor arcs, the arbitrary applications of firing rule may cause a contradictory situation. We suggest two directions to avoid contradictions: greedy and secure applications of firing rule. We choose the secure application and show that this is a direct translation of the well-founded semantics in the net model. Furthermore, we show that the greatest unfounded set corresponds to the greatest siphon in Petri net theory when we delete the transitions disabled by the secure application of firing rule, and that the property of siphon simplifies the computation of well-founded semantics for logic programs. We also propose the reduced-Petri-net method by which we can reduce an extended Petri net to a Petri net without inhibitor arcs and compute the well-founded model by iterative applications of this transformation using conventional application of firing rule.>

An extended Petri net is used to model function-free logic programs with negation, i.e. normal logic programs. In this model, because of the presence of inhibitor arcs, the arbitrary application of firing rules may cause a contradictory situation. The authors suggest two directions to avoid contradictions, greedy and secure application of firing rules. Secure application is a direct translation of the well-founded semantics in the net model. Furthermore, the authors show that an unfounded set corresponds to a siphon in Petri net theory when one deletes the transitions disabled by the secure application of firing rules, and that the property of siphons simplifies the computation of well-founded semantics for logic programs.>