A Petri net semantics for logic programs with negation

Abstract

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.<>