Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What the things are is not important, nor is what it means for them to be desirable. It can be applied to gambles, calling them desirable if a subject accepts them, but it can just as well be applied to pizzas, calling them desirable if my friend Arthur likes to eat them. Other useful examples of things one might apply this theory to are propositions, horse lotteries, or preferences between any of the above. Regardless of the particular things that are considered, inference rules are imposed by means of an abstract closure operator, and models that adhere to these rules are called coherent. I consider two types of models, each of which can capture a subject's beliefs about which things are desirable: sets of desirable things and sets of desirable sets of things. A crucial result is that the latter type can be represented by a set of the former.
翻译:受用于建模不确定性的不精确概率领域中的“期望赌局”理论启发,我提出了一种“需求物理论”。该理论旨在建模主体对事物需求性的信念。事物本身的性质无关紧要,其“需求性”的含义亦不关键。该理论可应用于赌局——若主体接受某个赌局,则称其具有需求性;它同样可应用于披萨——若我的朋友亚瑟喜欢吃某种披萨,则称其具有需求性。其他可能应用该理论的实例包括命题、马票,或前述任意事物之间的偏好关系。无论考虑的具体事物为何,都通过抽象闭包算子施加推理规则,遵循这些规则的模型称为“相干模型”。我考察了两类模型,每类均可捕捉主体对事物需求性的信念:需求事物集与需求事物集族。关键结论是,后一类模型可通过前一类模型进行表征。