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This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (⊤), that is revised to the(More)
We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams' conditional logic and are exactly the rules that preserve a natural, logical structure over(More)
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(More)
In this paper, we compare and contrast two methods for revising qualitative (viz., " full ") beliefs. The first method is a naïve Bayesian one, which operates via conditionalization and the minimization of expected inaccuracy. The second method is the AGM approach to belief revision. Our aim here is to provide the most straightforward explanation of the(More)
What is the relationship between degrees of belief and (all-or-nothing) beliefs? Can the latter be expressed as a function of the former, without running into paradoxes? We reassess this " belief-binarization " problem from the perspective of judgment-aggregation theory. Although some similarities between belief binarization and judgment aggregation have(More)