New journal paper: Accept & reject statement-based uncertainty models
Accept & reject statement-based uncertainty models (preprint pdf)
by Erik Quaeghebeur, Gert de Cooman and Filip Hermans
A paper with a long history, polished to perfection. It was conceived out of our frustration with the term ‘desirability’, and its lack of an operational definition. Whereas it is easy to see what it means to accept a gamble, it seems harder to define what it means to find it desirable, or strictly preferable to the status quo. We solve this problem by also looking at what it means to reject a gamble. And in doing so, we come up with a decision-based uncertainty theory that encompasses most of the existing ones in the literature, and which allows us to compare them and put them into proper perspective.
Abstract: We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or favourability and clarifies their relative position. Next to the statement-based formulation, we also provide a translation in terms of preference relations, discuss—as a bridge to existing frameworks—a number of simplified variants, and show the relationship with prevision-based uncertainty models. We furthermore provide an application to modelling symmetry judgements.
Published where? International Journal of Approximate Reasoning 59 (2015) 61–102.