A Triple Uniqueness of the Maximum Entropy Approach

Inductive logic is concerned with assigning probabilities to sentences given probabilistic constraints. The Maxium Entropy Approach to inductive logic I here consider assigns probabilities to all sentences of a first order predicate logic. This assignment is built on an application of the Maximum Entropy Principle, which requires that probabilities for uncertain inference have maximal Shannon Entropy. This paper puts forward two different modified applications of this principle to first order predicate logic and shows that the original and the two modified applications agree in many cases. A third promising modification is studied and rejected.