Asymptotic conditional probabilities for binary probability functions

Abstract

The paper investigates the class of probability functions defined on sentences of a predicate language containing binary and possibly also unary predicates which satisfy the Principle of Binary Exchangeability (a strengthening of the Principle of Exchangeability). Following a survey of relevant properties of such functions we prove the main theorems of this paper showing that under some mild conditions any such probability function can, by conditioning on suitable sentences, closely approximate any other probability function from this class. These results on conditioning extend earlier results obtained for purely unary languages.