Inheritance Theory and Networks with Roles

Abstract We present a formalization of monotonic inheritance nerworks with roles. Roles (like the role father) are partial functions from individuals to individuals and figure in universal-existential statements like “every person has a father.” The networks we consider also permit relational statements such as “every person's father loves that person's mother,” and equality statements among roles and individuals. Restricted networks of this sort are less expressive than first-order logic; like all inheritance systems, they constitute a sort of weak logic founded on path-based reasoning. On the other hand, their rules of inference and resulting proofs are substantially more complex than what one finds in simple IS-A hierarchies; the latter use purely linear proof sequences. We show all that query answering in networks with roles corresponds to parsing a fragment of the network with a context-free grammar whose nonterminals are inference rules and whose terminals are links. Proofs in these systems, although still path-based, take the form of trees rather than chains.