Semantics for Probabilistic Inference
This work addresses foundational issues in probabilistic reasoning for AI and logic, offering a formal framework for handling uncertain inferences, though it appears incremental relative to existing semantics.
The paper tackles the problem of formalizing nonmonotonic probabilistic inferences where conclusions are supported only to a certain degree, and it provides syntactic and semantic characterizations for such inferences, including standards for high-probability and interval-based support.
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.