An extended Petri net model for normal logic programs

Abstract
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 in this paper 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.

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