Boolean代数的Bayesian算子推广；应用于 一个确定性贝叶斯逻辑的定义

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摘要翻译：
本文的工作对布尔代数和贝叶斯概率的领域做出了贡献，提出了一个布尔代数的代数扩张，它实现了贝叶斯条件推理的一个算子，并在该算子下闭。自从刘易斯的工作（刘易斯的琐碎性）以来，我们知道在事件空间内不可能构造这样的条件算子。然而，这项工作提出了一个答案，通过在事件空间之外构造一个条件算子来补充刘易斯的琐碎性，从而产生了一个代数扩张。特别地，证明了在布尔代数上定义的任何概率都可以按照条件概率的乘法定义推广到它的代数扩张。在本文的最后一部分，在此代数扩张的基础上引入了一个新的二价逻辑，并导出了基本性质。
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英文标题：
《Extension of Boolean algebra by a Bayesian operator; application to the
  definition of a Deterministic Bayesian Logic》
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作者：
Frederic Dambreville (ENSIETA)
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最新提交年份：
2011
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分类信息：

一级分类：Mathematics        数学
二级分类：Logic        逻辑
分类描述：Logic, set theory, point-set topology, formal mathematics
逻辑，集合论，点集拓扑，形式数学
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Logic in Computer Science        计算机科学中的逻辑
分类描述：Covers all aspects of logic in computer science, including finite model theory, logics of programs, modal logic, and program verification. Programming language semantics should have Programming Languages as the primary subject area. Roughly includes material in ACM Subject Classes D.2.4, F.3.1, F.4.0, F.4.1, and F.4.2; some material in F.4.3 (formal languages) may also be appropriate here, although Computational Complexity is typically the more appropriate subject area.
涵盖计算机科学中逻辑的所有方面，包括有限模型理论，程序逻辑，模态逻辑和程序验证。程序设计语言语义学应该把程序设计语言作为主要的学科领域。大致包括ACM学科类D.2.4、F.3.1、F.4.0、F.4.1和F.4.2中的材料；F.4.3（形式语言）中的一些材料在这里也可能是合适的，尽管计算复杂性通常是更合适的主题领域。
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英文摘要：
  This work contributes to the domains of Boolean algebra and of Bayesian probability, by proposing an algebraic extension of Boolean algebras, which implements an operator for the Bayesian conditional inference and is closed under this operator. It is known since the work of Lewis (Lewis' triviality) that it is not possible to construct such conditional operator within the space of events. Nevertheless, this work proposes an answer which complements Lewis' triviality, by the construction of a conditional operator outside the space of events, thus resulting in an algebraic extension. In particular, it is proved that any probability defined on a Boolean algebra may be extended to its algebraic extension in compliance with the multiplicative definition of the conditional probability. In the last part of this paper, a new bivalent logic is introduced on the basis of this algebraic extension, and basic properties are derived.
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PDF链接：
https://arxiv.org/pdf/1109.6402

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关键词：Bayesian BOOLEAN Bayes baye Lean 答案 乘法 事件 可能 扩张