The Logical Postulates of Böge, Carnap and Johnson in the Context of Papangelou Processes

We adapt Johnson’s sufficiency postulate, Carnap’s prediction invariance postulate and Böge’s learn-merge invariance to the context of Papangelou processes and discuss equivalence of their generalizations, in particular their weak and strong generalizations. This discussion identifies a condition which occurs in the construction of Papangelou processes. In particular, we show that these generalizations characterize classes of Poisson and Pólya point processes.