Parsimonious set representations of orders, a generalization of the interval order concept, and knowledge spaces

摘要

Partial orders can be represented by subsets of a given set ordered by inclusion. Special kinds of such set representations are investigated because they facilitate the exploration of properties of knowledge spaces. A new type of order relation is defined which is closely related to interval orders. These orders and the interval orders are investigated with respect to their parsimonious set representations. The theorems are applied to knowledge space theory.