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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.

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