A Preorder Classiication Algorithm Based on a Poset Classiication Algorithm

This work shows how any classiication system based on orders may be extended to pre-orders. Such systems build hierarchies of object representations with a strict ordering relation between them and do not provide for the retention of multiple logically equivalent representations. In some domains retention of equivalent representations is required-this arises for example when integrating knowledge bases with diierent names for the same concepts. This requires extending order classiication to preorder classiication. Any preorder relation may be represented as an order of equivalence classes. Existing order classiication algorithms may be used to classify the equivalence classes so the extension to preorders is straightforward and may be applied to any order classiication algorithms that support ordered abstract objects.