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A logic for arguing about probabilities in measure teams

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Abstract

We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy–Weinberg Principle of biology and the Bell’s Inequalities of quantum physics as examples.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Tapani Hyttinen, Gianluca Paolini & Jouko Väänänen

  2. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Jouko Väänänen

Authors
  1. Tapani Hyttinen
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  2. Gianluca Paolini
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  3. Jouko Väänänen
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Corresponding author

Correspondence to Gianluca Paolini.

Additional information

The research of the second author was supported by the Finnish Academy of Science and Letters (Vilho, Yrjö and Kalle Väisälä foundation).

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Hyttinen, T., Paolini, G. & Väänänen, J. A logic for arguing about probabilities in measure teams. Arch. Math. Logic 56, 475–489 (2017). https://doi.org/10.1007/s00153-017-0535-x

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  • DOI: https://doi.org/10.1007/s00153-017-0535-x

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