6. The method of claim 2 , wherein at least one attributive expression contains at least one of: a) an intersection of attributes of different criteria; b) an intersection of the unions or complements of unions; wherein each union or complement of union is composed of the attributes of single criterion with no other union or complement of union in the intersection based on the same single criterion; c) a union of the intersection of attributes or complements of attributes, wherein each intersection is composed of the attributes of different criteria and no one intersection includes another intersection from the same union; or d) a union of the intersections of unions or complements of unions; wherein each union or complement of union is composed of the attributes of a single criterion with no other union or complement of union in the same intersection based on the same single criterion, and no one intersection includes another intersection from the same union.
2. A computer-implemented method for building a polyhierarchical classification of objects, comprising: a) identifying a plurality of criteria for specializing the objects based on their properties, wherein each criterion of the plurality of criteria is defined by a set of mutually exclusive attributes, wherein each attribute describes one or more properties of the objects; b) recurrently defining a root category for each criterion in terms of an attributive expression representing a logical composition of one or more attributes of criteria whose root categories have been previously defined in the recurrent sequence, or the empty attributive expression; wherein no one criterion participates in the definition of its own root category, and each attributive expression encodes a sequence of specializations by criteria so that the root category of each following criterion includes the category represented by the sequence of all previous specializations; c) storing in a computer-readable medium the plurality of criteria and their root categories in the form of attributive expressions; and d) using the stored plurality of criteria for polyhierachically structuring, updating and accessing information associated with the objects.