论文标题
复合条件作为随机数量和布尔代数
Compound conditionals as random quantities and Boolean algebras
论文作者
论文摘要
有条件在逻辑和概率推理的不同领域起着关键作用，并且已经从不同角度进行了研究和形式化。在本文中，我们关注了Finetti的条件概念，作为一个基于投注的语义的三值对象，其相关方法是主要由两位作者开发的随机数量。在文献中已经研究了复合条件，但并非完全普遍。在本文中，我们提供了一种自然程序，将有条件的随机量显式地附加到任意化合物条件上，这也使我们能够计算其预防。通过研究这些随机数量的性质，我们表明，实际上，可以将一组复合条件赋予布尔代数结构。在此过程中，我们为在三个价值条件的悠久传统与最新的建议将有条件作为合适布尔代数的元素视为有条件的提议之间铺平了道路。
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued object, with betting-based semantics, and its related approach as random quantity as mainly developed by two of the authors. Compound conditionals have been studied in the literature, but not in full generality. In this paper we provide a natural procedure to explicitly attach conditional random quantities to arbitrary compound conditionals that also allows us to compute their previsions. By studying the properties of these random quantities, we show that, in fact, the set of compound conditionals can be endowed with a Boolean algebraic structure. In doing so, we pave the way to build a bridge between the long standing tradition of three-valued conditionals and a more recent proposal of looking at conditionals as elements from suitable Boolean algebras.
