Tractable theories of multiple defeasible inheritance in ordinary nonmonotonic logics

A suggestion by John McCarthy for general formulations of multiple defeasible inheritance in ordinary nonmonotonic logic is examined and found to suffer from a variety of technical problems, including 1) its restriction to object/class/property networks, 2) unintuitive results in "Nixon diamond"-type networks, 3) unnecessary closed-world assumptions, and 4) susceptibility to unintended models when generalized. A family of theories is presented that substantially revises McCarthy's formulation to avoid these problems and restrictions. Finally, an inference control strategy for computing the theory is identified whose tractability is ensured by a variety of techniques including incremental computation of abnormalities and truth maintenance.