Propositional Logic, Nonmonotonic Reasoning and Symmetric Networks — On Bridging the Gap Between Symbolic and Connectionist Knowledge Representation

This chapter discusses the relationships between propositional logic and symmetric connectionist networks. The task is two-fold: 1) to develop a framework for reasoning with inconsistency that can be implemented on connectionist networks; 2) to develop a high-level language that may be used as an intermediate level of abstraction between symbolic description and low-level connectionist implementation. The article shows how to represent arbitrary logic formulas using symmetric networks and how logic can be used as a specification language for such networks. Propositional calculus is extended by augmenting beliefs with real positive penalties. The extended logic is capable of representing nonmonotonic knowledge as well as of coping with inconsistency in the knowledge base. Every formula in the extended logic can be compiled into a network, and every network can be described by a formula of the logic. Efficient algorithms are given to translate between the two forms of knowledge representation.