Lopez-Wild, Josiah (2024) Computable Qualitative Probability. [Preprint]
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Abstract
Theories of qualitative probability provide a justification for the use of numerical probabilities to represent an agent's degrees of belief. If a qualitative probability relation satisfies a set of well-known axioms then there is a probability measure that is compatible with that relation. In the particular case of subjective probability this means that we have sufficient conditions for representing an agent as having probabilistic beliefs. But the classical results are not constructive; there is in no general method for calculating the compatible measure from the qualitative relation. To address this problem this paper introduces the theory of computable qualitative probability. I show that there is an algorithm that computes a probability measure from a qualitative relation in highly general circumstances. Moreover I show that given a natural computability requirement on the qualitative relation the resulting probability measure is also computable. Since computable probability is a growing interest in Bayesian epistemology this result provides a valuable interpretation of that notion.
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| Item Type: | Preprint | ||||||
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| Keywords: | Qualitative probability, comparative probability, Bayesian epistemology, computability, computable analysis, probability theory | ||||||
| Subjects: | General Issues > Decision Theory Specific Sciences > Probability/Statistics |
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| Depositing User: | Mr. Josiah Lopez-Wild | ||||||
| Date Deposited: | 28 Aug 2024 03:37 | ||||||
| Last Modified: | 28 Aug 2024 03:37 | ||||||
| Item ID: | 23841 | ||||||
| Subjects: | General Issues > Decision Theory Specific Sciences > Probability/Statistics |
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| Date: | 2024 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23841 |
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