Establish the Three Theorems: Brain-Like DNs Logically Reason and Optimally Generalize

In artificial intelligence (AI) there are two major schools, symbolic and connectionist. Weng 2011 [6] proposed three major properties of the Developmental Network (DN) which bridged the two schools: (1) From any complex FA that demonstrates human knowledge through its sequence of the symbolic inputs-outputs, the DP incrementally develops a corresponding DN through the image codes of the symbolic inputs-outputs of the FA. The DN learning from the FA is incremental, immediate and error-free. (2) After learning the FA, if the DN freezes its learning but runs, it generalizes optimally for infinitely many image inputs and actions based on the embedded inner-product distance, state equivalence, and the principle of maximum likelihood. (3) After learning the FA, if the DN continues to learn and run, it “thinks” optimally in the sense of maximum likelihood based on its past experience. This paper presents the three major theorems and their proofs.