A Theoretical Framework for a Knowledge Programming System Based on Default Logic and Its Program Transformation

Abstract

This paper propose a theoretical framework for a knowledge programming system based on Reiter's default logic, where knowledge including complicated exceptions can be expressed simply as a default without enumerating exceptions explicitly. For this framework, we introduce a default theory called a normal Horn default theory and two kinds of constraints for the extensions of the default theory, called negative and positive constraints. Knowledge is represented using the normal Horn default theory and the two constraints. An inference of a default theory is usually very inefficient because of its non-monotonicity. To resolve this situation, we also give a program transformation method that incorporates the constraints into the normal Horn default theory. An inference of a normal default theory is achieved monotonically. Thus the program transformation yields an optimized knowledge program.