HYPOTHESIS AND THEORY article
Front. Cognit.
Sec. Reason and Decision-Making
Volume 4 - 2025 | doi: 10.3389/fcogn.2025.1623227
This article is part of the Research TopicCausal Cognition in Humans and Machines - Volume IIView all 6 articles
Commutativity of Probabilistic Belief Revision
Provisionally accepted
- Radboud University, Nijmegen, Netherlands
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Bayesian updating, also known as belief revision or conditioning, is a core mechanism of probability theory, and of AI. The human mind is very sensitive to the order in which it is being 'primed', but Bayesian updating works commutatively: the order of the evidence does not matter. Thus, there is a mismatch. This paper develops Bayesian updating as an explicit operation on (discrete) probability distributions, so that the commutativity of Bayesian updating can be clearly formulated and made explicit in several examples. The commutativity mismatch is underexplored, but plays a fundamental role, for instance in the move to quantum cognition.
Keywords: Bayesian updating, Multiset, Commutativity, notation, Cognition
Received: 05 May 2025; Accepted: 25 Jun 2025.
Copyright: © 2025 Jacobs. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Bart Jacobs, Radboud University, Nijmegen, Netherlands
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