Rule-Based Reasoning in Connectionist Networks

Abstract

This thesis addresses the problem of efficiently representing large knowledge bases and performing a class of inferences extremely fast. The speed of reasoning depends on a number of factors including the expressiveness of the system, the nature of the computational architecture and the representation methodology. A number of knowledge representation and reasoning schemes have given very high emphasis to just one of such issues while neglecting others. This dissertation work is based on the belief that it is beneficial to take an approach where all such issues are simultaneously addressed. With respect to the issue of computational architecture, it is argued that a connectionist architecture has some significant advantages. Having made that choice, we explore how to represent and reason with rules involving multi-place predicates and variables in a connectionist architecture. The main hurdle that needs to be crossed in order to be able achieve this is the dynamic binding problem. In essence, the problem is that of representing the dynamic grouping of nodes located in different parts of the network. We use what we refer to as the synchronous activation approach to solve the binding problem. Simply stated, the idea is just that the dynamic grouping of a set of nodes is represented by the fact that all those nodes fire synchronously. This happens to be a solution that is technically attractive as well as biologically plausible. Incorporating the synchronous activation approach to solve the binding problem, rulebased forward and backward reasoning systems have been designed to perform deductive inferences. These systems represent knowledge very efficiently: the number of nodes and links required is only linear in the size of the knowledge base. They also perform inferences extremely fast: an inference takes time that is just linear in the length of the shortest proof. We also examine various ways of extending the expressiveness and reasoning abilities of these systems. An alternative representation scheme more amenable to learning is also presented along with a proposal for doing abductive reasoning in connectionist networks.