The principal objects of the investigation reported were, first, to study qualitative probability relations on Boolean algebras, and secondly, to describe applications in the theories of probability logic, information, automata, and probabilistic measurement. The main contribution of this work is stated in 10 definitions and 20 theorems. The basic concern in this technical report was to show that probability, entropy, and information measures can be studied successfully in the spirt of representational or algebraic measurement theory. The method utilized in this report is based on the most general results of modern mathematics, which state a one-to-one correspondence among relations, cones in vector spaces, and the classes of positive functionals. (RP)