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

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Abstract

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.

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Acknowledgments

The authors thank the referee for carefully reading the manuscript and giving valuable comments.

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  1. Mathias Rafler

    Present address: Universität at Potsdam, Institutät für Mathematik, Am Neuen Palais 10, 14469 , Potsdam, Germany

Authors and Affiliations

  1. TU München, Zentrum Mathematik M5, Boltzmannstr. 3, 85747 , Garching bei München, Germany

    Mathias Rafler

  2. Fakultät für Mathematik der Universität Bielefeld, Postfach 10 01 31, 33601 , Bielefeld, Germany

    Hans Zessin

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  1. Mathias Rafler
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  2. Hans Zessin
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Correspondence to Mathias Rafler.

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Rafler, M., Zessin, H. The Logical Postulates of Böge, Carnap and Johnson in the Context of Papangelou Processes. J Theor Probab 28, 1431–1446 (2015). https://doi.org/10.1007/s10959-014-0543-2

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  • DOI: https://doi.org/10.1007/s10959-014-0543-2

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