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

TL;DR

This paper examines the adaptation and equivalence of classical logical postulates by B"oge, Carnap, and Johnson within the framework of Papangelou processes, revealing their connection to Poisson and Pólya point processes.

Contribution

It adapts and compares foundational logical postulates to Papangelou processes, identifying conditions that characterize Poisson and Pólya point processes.

Findings

Generalizations characterize classes of Poisson and Pólya point processes

Identifies a key condition in the construction of Papangelou processes

Shows equivalence of different logical postulate adaptations

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.