Does Probability Have a Place in Non-monotonic Reasoning?

The panel on uncertain reasoning at AAAI-84 considered the question of whether or not implementations of non-monotonic reasoning should be probabilistic. A variety of (generally unsupported) claims were made to the effect that probabilities arc unintuitive, that the numbers needed arc unavailable, and that the method generally is inappropriate. The counterclaims that probabilities are intuit ive, available and appropriate were similarly unsupported. My intention here is to present some results that deal wi th these questions. Let me stress that it is precisely the question posed in that last paragraph that interests me: Should probabilities be used to implement non-monotonic reasoning systems? The easier question of whether probabilities can be used to implement some types of non-monotoic reasoning has been answered rather conclusively by M Y C I N and its offspring; more difficult questions involving the nature or definition of probability itself have been grappled with by philosophers for centuries, and I am content to leave them to i t . I wi l l attempt to address the issues of whether the numbers required by a probabilistic theory can in general be made available to a reasoning system, and whether or not probabilistic methods arc effective. The first of these is principally a theoretical issue, while the second is more one of pragmatics.