A New Theory of Acceptance that Solves the Lottery Paradox and Provides a Simplified Probabilistic Semantics for Adams' Logic of Conditionals

A class of acceptance rules is proposed to relate probabilistic degrees of belief to acceptance. The rules avoid the lottery paradox and yield a probabilistic semantics (i) that adopts Ramsey test for accepting conditionals, (ii) that defines validity as preservation of acceptance, (iii) that allows acceptance under uncertainty; and (iv) that validates exactly Adams’ logic of flat conditionals. Furthermore, the rules illuminate a close relationship between two types of reasonings: the Bayesian reasoning by probabilistic conditioning can be represented as the nonmonotonic reasoning by ignoring less normal cases.