Probabilsitic semantics and defaults

There is much interest in providing proba-· bilistic semantics for defaults but most ap­ proaches seem to suffer from one of two prob­ lems: either they require numbers, a problem defaults were intended to avoid, or they gen­ erate peculiar side effects. Rather than provide semantics to defaults, we address the original problem that defaults were intended to solve: that of reasoning un­ der 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 confirmation, where a confirms b = coni( a, b) = p(a!b) > p(a). The formalism seems to handle the exam­ ples from the nonmonotonic literature. Most importantly, the sentences of our system can be verified by performing an appropriate ex­ periment in the semantic domain.