Regularity: generalizing inheritance to arbitrary hierarchies

Regularity is formalized from the general observation that hierarchical relationships between concepts reflect relationships between the concepts´ properties, and vice-versa. A procedure called expansion is utilized to compute property values when those are not known, based on the patterns of regularity. Inheriting property values in taxonomies is a special case of expansion. Expansion may fail in tangled hierarchies in the same way that multiple inheritance may lead to conflicting inferences in taxonomies. The definition of regularity and the expansion procedure have been extended to fuzzy sets. The fuzzy sets framework takes into account the normative nature of property values and handles cases where expansion fails. A procedure parametrically enlarges sets of property values so that expansion does not fail. A theorem describes the effect of the choice of the enlargement parameter on the reliability of expansion. Applications of regularity and expansion to the building and maintenance of hierarchies are discussed