Semantics for Probabilistic Inference

TL;DR

This paper formalizes nonmonotonic probabilistic inferences where conclusions are supported to varying degrees, providing semantic and syntactic characterizations for inferences with different levels of probabilistic support.

Contribution

It introduces a formal framework for nonmonotonic probabilistic inference with graded support, extending traditional logical inference to probabilistic contexts.

Findings

Characterizes probabilistic inferences with high support as valid.

Defines intermediate support inferences with partial validity.

Provides semantic and syntactic standards for probabilistic reasoning.

Abstract

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.