Irrelevance and Conditioning in First-Order Probabilistic Logic

Abstract

First-order probabilistic logic is a powerful knowledge representation language. Unfortunately, deductive reasoning based on the standard semantics for this logic does not support certain desirable patterns of reasoning, such as indifference to irrelevant information or substitution of constants into universal rules. We show that both these patterns rely on a first-order version of probabilistic independence, and provide semantic conditions to capture them. The resulting insight enables us to understand the effect of conditioning on independence, and allows us to describe a procedure for determining when independencies are preserved under conditioning. We apply this procedure in the context of a sound and powerful inference algorithm for reasoning from statistical knowledge bases. 1 Introduction First-order logic is widely recognized as being a fundamental building block in knowledge representation. As is well known, however, first-order logic does not have the necessary expressive po...