Probabilistic Inference and Non-Monotonic Inference
Henry E. Kyburg · 1989
Since the appearance of the influential article by McCarthy and Hayes, few people have tried to use probabilities as a basis for non-monotonic inference. One reason, perhaps the main one, is that probabilistic inference easily yields inconsistent bodies of knowledge, as is revealed by the lottery paradox. Here we establish three things: First, that standard systems of non-monotonic reasoning (default logic, non-monotonic logic, and circumscription) fall prey to the same lottery-like difficulties as does probabilistic inference. Second, that probabilistic inference provides equally plausible treatments of the standard examples of non-monotonic reasoning. Third, that the inconsistency threatened by the lottery paradox is a petty hobgoblin, and need not in any way interfere with the use of beliefs in planning and design.