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

摘要

We adapt Johnson's sufficiency postulate, Carnap's prediction invariancepostulate and B\"oge's learn-merge invariance to the context of Papangelouprocesses and discuss equivalence of their generalizations, in particular theirweak and strong generalizations. This discussion identifies a condition whichoccurs in the construction of Papangelou processes. In particular, we show thatthese generalizations characterize classes of Poisson and P\'olya pointprocesses.