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Semantics for Uncertain Inference Based on Statistical Knowledge

In: Mathematical Models for Handling Partial Knowledge in Artificial Intelligence

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  • Henry E. Kyburg Jr.

    (University of Rochester, Computer Science and Philosophy)

Abstract

In ordinary first order logic, a valid inference in a language L is one in which the conclusion is true in every model of the language in which the premises are true. To accommodate inductive/uncertain/probabilistic/non-monotonic inference, we weaken that demand to the demand that the conclusion be true in a large proportion of the models in which the relevant premises are true. More generally, we say that an inference is [p,q] valid if its conclusion is true in a proportion lying between p and q of those models in which the relevant premises are true. If we include a statistical variable binding operator “%” in our language, there are many quite general (and useful) things we can say about uncertain validity. A surprising result is that some of these things may conflict with Bayesian Conditionalization.

Suggested Citation

  • Henry E. Kyburg Jr., 1995. "Semantics for Uncertain Inference Based on Statistical Knowledge," Springer Books, in: Giulianella Coletti & Didier Dubois & Romano Scozzafava (ed.), Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pages 65-81, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1424-8_4
    DOI: 10.1007/978-1-4899-1424-8_4
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