论文标题
差距和间隙的概率
Probabilities with Gaps and Gluts
论文作者
论文摘要
Belnap-Dunn Logic（BD）有时也称为一级元素，是一个四值的命题逻辑，可以与两个非古典真实价值观相辅相成的真实和错误的经典真实价值。后两个是说明不完整信息或提供矛盾的证据的可能性。在本文中，我们提出了BD的概率扩展，允许代理人对命题的真理和虚假性具有概率的信念。我们为定义的框架提供了声音和完整的公理化，并确定了条件化和聚合的策略。具体而言，我们引入了贝叶斯和杰弗里更新的四个值等效物，并提出了从不同来源汇总信息的机制。
Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes' and Jeffrey updating and also suggest mechanisms for aggregating information from different sources.
