Determining Maximal Entropy Functions for Objective Bayesian Inductive Logic

Abstract According to the objective Bayesian approach inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy premisses, satisfies conclusion. When and are constraints on probabilities of sentences first-order predicate language, however, it is by no means obvious how determine these entropy functions. This paper makes progress problem in following ways. Firstly, we introduce concept limit show that, if set functions satisfying contains then this point unique function. Next, turn special case which categorical logical language. We uniform gives positive probability, can be found simply conditionalising prior premisses. generalise our results demonstrate agreement between Jeffrey conditionalisation there single premiss specifies sentence after learning such premiss, certain inferences preserved, namely tautologies. Finally, consider potential pathologies approach: explore extent invariant under permutations constants discuss some cases