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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2603.04188 |
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| _version_ | 1866908866082504704 |
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| author | Aambø, Torgeir |
| author_facet | Aambø, Torgeir |
| contents | Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired by work of Opdan, we introduce a general category theoretic definition of epistemic calculi, which we use as a foundation for modelling and studying contradictions and synergies between several philosophical epistemological concepts. We further develop an enriched category theoretic process for changing calculi, and use this to study relationships between existing examples, like possibility theory and certainty factors. Finally, we introduce a general categorical form of belief updating based on change of enrichment, and prove that Bayesian updating and possibilistic conditioning arise as examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A categorical formalization of epistemic uncertainty frameworks Aambø, Torgeir Category Theory Probability 68T37, 18D20, 18M05 Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired by work of Opdan, we introduce a general category theoretic definition of epistemic calculi, which we use as a foundation for modelling and studying contradictions and synergies between several philosophical epistemological concepts. We further develop an enriched category theoretic process for changing calculi, and use this to study relationships between existing examples, like possibility theory and certainty factors. Finally, we introduce a general categorical form of belief updating based on change of enrichment, and prove that Bayesian updating and possibilistic conditioning arise as examples. |
| title | A categorical formalization of epistemic uncertainty frameworks |
| topic | Category Theory Probability 68T37, 18D20, 18M05 |
| url | https://arxiv.org/abs/2603.04188 |