Seonglae Cho- Belief (degree of plausibility) is represented by a real number
- Divisibility and comparability - The plausibility of a proposition is a real number and is dependent on information we have related to the proposition.
- Qualitative correspondence with common sense, and with logic
- Common sense – Plausibilities should vary sensibly with the assessment of plausibilities in the model.
- Consistency – If the plausibility of a proposition can be derived in many ways, all the results must be equal.
These Axioms as Desiderata can results
- Additivity Rule / Sum rule - Marginalization
- Multiplication Rule / Product rule - Bayes Theorem
Chain rule is a generalization of the product rule
Product rule to Bayes Theorem
Cox's theorem
Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates.[1][2] This derivation justifies the so-called "logical" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition. Logical (also known as objective Bayesian) probability is a type of Bayesian probability. Other forms of Bayesianism, such as the subjective interpretation, are given other justifications.
https://en.wikipedia.org/wiki/Cox's_theorem