An Application of Lattice Theoryto Knowledge

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 semantics of a simple knowledge representation language is presented. Then we show how to use Birkhoo's Representation Theorem for Finite Distributive Lattices to build incremen-tally what we call a Birkhoo implementation of a knowledge base by processing a sequence of terminological axioms. A mathematical proof of the correctness of our technique with respect to the given semantics is an integral part of the development. While the intended application is to knowledge representation, these methods can be used whenever a computationally tractable representation of a nite distributive lattice needs to be implemented.