Higher-Order Petri Net Models Based on Artificial Neural Networks

In this paper, the properties of higher-order neural networks are exploited in a new class of Petri nets, called higher-order Petri nets (HOPN). Using the similarities between neural networks and Petri nets this paper demonstrates how the McCullock-Pitts models and the higher-order neural networks can be represented by Petri nets. A 5-tuple HOPN is defined, a theorem on the relationship between the potential firability of the goal transition and the T-invariant (HOPN) is proved and discussed. The proposed HOPN can be applied to the polynomial clause subset of first-order predicate logic. A five-clause polynomial logic program example is also included to illustrate the theoretical results.