Probabilistic Semantics and Defaults

Abstract: There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side effects. Rather than provide semantics for defaults, we address the problem defaults were intended to solve: that of reasoning under uncertainty where numeric probability distributions are not available. We describe a non-numeric formalism called an inference graph based on standard probability theory, conditional independence and sentences of favouring where a favours b - favours(a, b) - p(a|b) > p(a). The formalism seems to handle the examples from the nonmonotonic literature. Most importantly, the sentences of our system can be verified by performing an appropriate experiment in the semantic domain.