Algebraic properties of knowledge representation systems

Abstract

New concepts of knowledge representation systems, like object and attribute factors, connectedness relations, and seven kinds of homomorphisms of knowledge representation systems are introduced. Some properties of these homomorphisms, related to factors and connectedness, are shown. The theory presented here may be used to aggregate sets of objects, attributes, and descriptors of the original system in order to produce a simpler system, which preserves the description function of the original system. In some applications, the new system is sufficient representation of the original one.