# From Propositional Logic to Plausible Reasoning: A Uniqueness Theorem

arXiv: https://arxiv.org/abs/1706.05261 · HTML: https://mlsanity.com/paper/1706.05261/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools](https://mlsanity.com/paper/2606.20740/) (2026)

## Abstract (arXiv)

We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be preserved in the extended logic; as such, the requirements are simpler and less problematic than those used in Cox's Theorem and its variants. As with Cox's Theorem, our requirements imply that the extended logic must be isomorphic to (finite-set) probability theory. We also obtain specific numerical values for the probabilities, recovering the classical definition of probability as a theorem, with truth assignments that satisfy the premise playing the role of the "possible cases."