Can logic be combined with probability? Probably

AbstractIn the nineteen sixties seminal work was done by Gaifman and then Scott and Krauss in adapting the concepts, tools and procedures of the model theory of modern logic to provide a corresponding model theory in which notions of probabilistic consistency and consequence are defined analogously to the way they are defined (semantically) in the deductive case. The present paper proposes a way of extending these ideas beyond the bounds of a formalised language, even the infinitary language of Scott and Krauss, to achieve a logic having the power and expressiveness of the modern mathematical theory of probability