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We develop a framework for modelling and reasoning with uncertainty based onaccept and reject statements about gambles. It generalises the frameworks foundin the literature based on statements of acceptability, desirability, orfavourability and clarifies their relative position. Next to thestatement-based formulation, we also provide a translation in terms ofpreference relations, discuss---as a bridge to existing frameworks---a numberof simplified variants, and show the relationship with prevision-baseduncertainty models. We furthermore provide an application to modelling symmetryjudgements.

Accept & Reject Statement-Based Uncertainty Models