The logical postulates of B\"oge, Carnap and Johnson in the context of Papangelou processes

Abstract

We adapt Johnson's sufficiency postulate, Carnap's prediction invariance postulate and B\"oge'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 P\'olya point processes.