Title: From Propositional Logic to Plausible Reasoning: A Uniqueness Theorem,
Abstract: 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."