Problems with Parts

Abstract

Two problems in representing and using relationships among parts of objects are analysed, and partial solutions are proposed. The first is the problem of extracting information from over lapping partitioning hierarchies. Contrary to a common assumption, part-of relationships cannot be extracted from arbitrary sets of partitioning assertions by simple label-propagation methods: the problem is in general NP-complete. However, if the lowest-level parts of all entities under consideration are drawn from a common pool of pairwise disjoint ultimate parts, then relatively simple, complete inference methods for deriving part -of and other relationships can be supplied. The second problem is that of property inheritance, i.e., the transfer of relationships among parts of a generic object to corresponding parts of a successor of that object in the type hierarchy. Earlier solutions are criticized and a new solution based on function tables attached to concepts is proposed.