主观概率、三价逻辑与复合条件
Subjective probability, trivalent logics and compound conditionals
摘要：
在这项工作中，我们首先说明了主观理论的德Finetti。通过考虑无条件和有条件的情况，我们回顾了投注方案和惩罚标准的一致性概念。我们通过给出相干性的几何解释证明了这两个判据的等价性。我们还考虑了基于适当的评分规则的一致性的概念。我们讨论的条件事件的三价逻辑的de Finetti和真值的数值表示。我们检查的有效性选定的基本逻辑和概率性质的一些三价逻辑：Kleene-Lukasiewicz-Heyting-de Finetti; Lukasiewicz; Bochvar-Kleene; Sobocinski。我们验证了这些逻辑都不满足所有的性质。然后，我们考虑我们的方法，在条件随机量的设置条件事件的合取和析取。我们验证了所有的基本逻辑和概率属性（包括Fréchet-Hoeffding界限）在我们的方法中得到保留。我们还回顾了我们的合取概念对p-相容性和p-蕴涵的刻画。
英文摘要：
In this work we first illustrate the subjective theory of de Finetti. We recall the notion of coherence for both the betting scheme and the penalty criterion, by considering the unconditional and conditional cases. We show the equivalence of the two criteria by giving the geometrical interpretation of coherence. We also consider the notion of coherence based on proper scoring rules. We discuss conditional events in the trivalent logic of de Finetti and the numerical representation of truth-values. We check the validity of selected basic logical and probabilistic properties for some trivalent logics: Kleene-Lukasiewicz-Heyting-de Finetti; Lukasiewicz; Bochvar-Kleene; Sobocinski. We verify that none of these logics satisfies all the properties. Then, we consider our approach to conjunction and disjunction of conditional events in the setting of conditional random quantities. We verify that all the basic logical and probabilistic properties (included the Fréchet-Hoeffding bounds) are preserved in our approach. We also recall the characterization of p-consistency and p-entailment by our notion of conjunction.
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