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Can logic be combined with probability? Probably

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In 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.

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en

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http://eprints.lse.ac.uk/30254/

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