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Equivalent conditional probability systems
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DOI：10.1007/s11229-025-05433-5.png)
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Abstract
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By defining conditional probabilities as primitives, R & eacute;nyi (Acta Mathematica Academiae Scientiarum Hungaricae 6(3):285-335, 1955) provides a framework for understanding scenarios that challenge classical probability theory, such as conditioning on events with zero unconditional probability. The paper proposes a notion of equivalence among such conditional probability systems (CPSs) and shows its appealing properties (e.g., the existence of a canonical form). Additionally, we demonstrate an application of the equivalence concept by continuing the work started in Brandenburger et al. (Synthese 201(5):175, 2023) to show that, at some fundamental level, lexicographic probability systems (LPSs) and finitary CPSs are merely different ways of encoding the same probabilistic information.
Keywords:
Conditional probability systems
Equivalence
Lexicographic probability systems
Belief revision
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