Semantics for Probabilistic Inference
  A number of writers(Joseph Halpern and Fahiem Bacchus among them) have
offered semantics for formal languages in which inferences concerning
probabilities can be made. Our concern is different. This paper provides a
formalization of nonmonotonic inferences in which the conclusion is supported
only to a certain degree. Such inferences are clearly 'invalid' since they must
allow the falsity of a conclusion even when the premises are true.
Nevertheless, such inferences can be characterized both syntactically and
semantically. The 'premises' of probabilistic arguments are sets of statements
(as in a database or knowledge base), the conclusions categorical statements in
the language. We provide standards for both this form of inference, for which
high probability is required, and for an inference in which the conclusion is
qualified by an intermediate interval of support.
