COMBINATORIAL SEMANTICS - SEMANTICS FOR FREQUENT VALIDITY

In ordinary first-order logic, a valid inference in a language L is on e in which the conclusion is true in every model of the language in wh ich the premises are true. To accommodate inductive/uncertain/probabil istic/nonmonotonic inference, we weaken that demand to the demand that the conclusion be true in a large proportion of the models in which t he relevant premises are true. More generally, we say that an inferenc e is [p, q] valid if its conclusion is true in a proportion lying betw een p and q of those models in which the relevant premises are true. I f we include a statistical variable binding operator ''%'' in our lang uage, there are many quite general (and useful) things we can say abou t uncertain validity. A surprising result is that some of these things may conflict with Bayesian conditionalization.