An application of lattice theory to knowledge representation

The goal of this paper is to show how ideas from lattice theory can be used in the implementation of a knowledge representation language. First, the s emantics of a simple knowledge representation language is presented. Then w e show how to use Birkhoffs Representation Theorem for finite distributive lattices to build incrementally what we call a Birkhoff implementation of a knowledge base by processing a sequence of terminological axioms. A mathem atical proof of the correctness of our technique with respect to the given semantics is an integral part of the development. While the intended applic ation is to knowledge representation, these methods can be used whenever a computationally tractable representation of a finite distributive lattice n eeds to be implemented. (C) 2000 Elsevier Science B.V. All rights reserved.