The Petri net models of the clauses for logical inference using fixpoint are studied and the four-valued logic and the conflict transition concept are introduced. The authors can construct the Petri net models of non-Horn clauses based on the models of Horn clauses. Finding the fixpoint of logical values is one of the fundamental methods for logical inference. In this paper, an algorithm for the fixpoint based on the Petri net models of values is presented, and it is more efficient than the previous ones.