Conceptual Entities.

Discussed is one "quite general" attribute that can differentiate problem representations: the kinds of entities that are included -- the cognitive objects that the system can reason about in a relatively direct way, and that are included continuously in the representation. The ontology of a domain is significant for four reasons. First, ontology is a significant factor in forming analogies between domains, described in terms of two examples involving problem-solving procedures between domains: geometric proofs and subtraction procedures. Second, these entities provide arguments on which general reasoning procedures can operate directly; this is explored through physics problems; distance, time, and velocity; and sound transmission. That conceptual entities can enable more efficient computation is presented in terms of monster problems, isomorphic to the Tower of Hanoi problem. Finally, the ontology of a problem domain has important effects on goal definition and planning, illustrated by studies of binomial probability. (MNS)