Commutativity of probabilistic belief revision
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...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-08-01
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| Series: | Frontiers in Cognition |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fcogn.2025.1623227/full |
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| author | Bart Jacobs |
| author_facet | Bart Jacobs |
| author_sort | Bart Jacobs |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5f0de04a88e642f7a34e2001a3444719 |
| institution | Kabale University |
| issn | 2813-4532 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Cognition |
| spelling | doaj-art-5f0de04a88e642f7a34e2001a34447192025-08-20T04:02:13ZengFrontiers Media S.A.Frontiers in Cognition2813-45322025-08-01410.3389/fcogn.2025.16232271623227Commutativity of probabilistic belief revisionBart JacobsBayesian 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.https://www.frontiersin.org/articles/10.3389/fcogn.2025.1623227/fullBayesian updatingmultisetcommutativitynotationcognition |
| spellingShingle | Bart Jacobs Commutativity of probabilistic belief revision Frontiers in Cognition Bayesian updating multiset commutativity notation cognition |
| title | Commutativity of probabilistic belief revision |
| title_full | Commutativity of probabilistic belief revision |
| title_fullStr | Commutativity of probabilistic belief revision |
| title_full_unstemmed | Commutativity of probabilistic belief revision |
| title_short | Commutativity of probabilistic belief revision |
| title_sort | commutativity of probabilistic belief revision |
| topic | Bayesian updating multiset commutativity notation cognition |
| url | https://www.frontiersin.org/articles/10.3389/fcogn.2025.1623227/full |
| work_keys_str_mv | AT bartjacobs commutativityofprobabilisticbeliefrevision |