有缺口和过剩的概率
Probabilities with Gaps and Gluts
摘要：
贝尔纳普-邓恩逻辑（英语：Belnap-Dunn logic，BD），有时也被称为一级蕴涵，是一种四值命题逻辑，它用两个非经典的真假值Neither和Both来补充真和假的经典真假值。后两项是为了说明现有资料可能不完整或提供相互矛盾的证据。在本文中，我们提出了一个概率的BD扩展，允许代理有概率信念的真理和虚假的命题。我们提供了一个健全的和完整的公理化的框架定义，并确定政策的条件化和聚合。具体地说，我们介绍了四值等价的贝叶斯和杰弗里更新，并建议从不同来源的信息聚合机制。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
