Complete inference via knowledge Petri nets and resolution rules

Abstract

A novel inference approach is presented based on knowledge Petri nets and resolution rules. First, a knowledge base is modeled as a knowledge Petri net, where logical clauses are represented by monitor places, called semantic places. Second, a resolution pair is defined to identify a pair of semantic places, which, corresponding to two clauses that can be resolved, can be used to generate a new place in the knowledge Petri net. Such a new place represents an unknown clause implied by the knowledge base. Third, a method is proposed to decide whether a resolution inference is redundant based on the resolution pair. The size of a knowledge Petri net can be reduced, and the inference computation is saved in this way. Fourth, an inference algorithm is proposed employing the resolution pair and knowledge Petri net, proven to be sound and complete. Its computational complexity is polynomial with respect to the number of logical variables and clauses. In addition, another inference algorithm is developed for a given complete knowledge base and a set of newfound clauses. The algorithm is proven to be sound and complete, which offers significantly reduced computational complexity and specifically is linear concerning the number of new clauses. Finally, the wumpus world problem is taken as an example to illustrate and verify the proposed inference algorithms.