TL;DR
This paper derives the core rules of probability theory from logical principles, addressing criticisms of Cox's approach and establishing a unique, consistent framework for rational belief measurement.
Contribution
It provides a derivation of probability rules as the only consistent representation of logical operations, bypassing the need for axiomatic justification.
Findings
Derives sum and product rules from logical consistency
Addresses criticisms of Cox's probability approach
Establishes uniqueness of probability representation
Abstract
Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there counterexamples to Cox? Rather than justifying Cox's choice of axioms we follow a different path and derive the sum and product rules of probability theory as the unique (up to regraduations) consistent representations of the Boolean AND and OR operations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.