On logical semantics of hybrid symbolic-neural networks for commonsense reasoning

Commonsense reasoning is an essential issue in knowledge representation, system dynamics modeling and information processing. However, logic based theories of commonsense reasoning always suffer from computational difficulties during their reasoning. For instance, even for a simple propositional case of default reasoning, the computation of a default theory´s extension is intractable. On the other hand, recent research shows that the hybrid symbolic-neural network (HSNN) has both specification and computational advantages in commonsense reasoning. However, the major shortcoming of this neural network, as argued by some researchers, is a lack of formal semantics. The purpose of this paper is to investigate formal semantics of HSNNs and show that under some formalization, a formal semantics is actually embedded within HSNNs