Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
A Predicate-Transition Net Model for Parallel Interpretation of Logic Programs
IEEE Transactions on Software Engineering
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Three-valued formalizations of non-monotonic reasoning and logic programming
Proceedings of the first international conference on Principles of knowledge representation and reasoning
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Foundations of disjunctive logic programming
Foundations of disjunctive logic programming
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
Contributions to the Theory of Logic Programming
Journal of the ACM (JACM)
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
A Petri Net Model for Reasoning in the Presence of Inconsistency
IEEE Transactions on Knowledge and Data Engineering
A formal modeling approach for supply chain event management
Decision Support Systems
Constraint-centric workflow change analytics
Decision Support Systems
Design of a high speed logic engine for distributed decision support systems
Intelligent Decision Technologies
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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.