A first-order probabilistic logic with approximate conditional probabilities

Abstract

We define a first-order probabilistic logic with Keisler-style probabilistic quantifiers allowing non-standard values of probabilistic functions. An axiomatic system with two infinitary rules of inference is given and proved to be sound and strongly complete. The decidability of two quite expressive fragments of this logic is proved. The fragments may be used to model not only the usual defaults but also a generalized version of defaults with several variables.