Petri net semantics of logic programs and deductive databases

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Joining concepts from database theory and logic programming leads to the theory of deductive databases, which store both extensional facts and rule-based knowledge about modeled real-world aspects. A deductive database management system (DDBMS) comprises an arbitrary database management system and a deduction mechanism that utilizes both extensional and intensional facts and rules to infer new data. A significant challenge in this field is finding a constructive semantics that aligns with users' intuitive interpretations of rules. This work introduces a Petri net semantics for logic programs and deductive databases, offering a more constructive approach than existing semantics. Logic programs and deductive databases are represented as a class of Petri nets, termed fixpoint nets, which express non-monotonic reasoning through generalized conflict situations. The semantics of a logic program or deductive database is determined by the logical consequences derived from a set of potentially three-valued models, generated from the saturated marking of the Petri net representation. It is demonstrated that for stratified normal programs and positive disjunctive programs, the Petri net semantics aligns with the perfect model semantics and Minker/Rajasekar semantics, respectively.