论文标题
条件，概率和逻辑的布尔代数
Boolean algebras of conditionals, probability and logic
论文作者
论文摘要
本文介绍了对条件事件的结构以及在这种情况下自然出现的概率度量的调查。特别是，我们引入了一种结构，该结构定义了任何（有限的）事件的（有限的）布尔代数（有限）{\ em boolean代数}。通过这样做，我们区分了依赖概率的条件事件的特性以及条件事件固有的属性属性。我们的主要结果提供了一种将标准的两位条件概率视为有条件事件的单位概率功能的方法。我们还考虑有条件的布尔代数的逻辑对应物，该代数与非单调推理的优先后果关系有联系。本文的总体框架为有条件知识表示逻辑与概率之间的丰富相互作用提供了一种新的观点。
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of conditionals} from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.
