摘要翻译：
连续逻辑对多值Lukasiewicz逻辑进行了扩展，在命题上增加了一个半算子。这种扩展的设计是为了给出一个更令人满意的连续结构的模型理论。这些逻辑的语义可以使用称为圈的代数结构的特殊形式来给出。作为对命题连续逻辑元理论研究的一部分，我们感谢Prover9找到了一个重要代数定律的证明。
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英文标题：
《(Dual) Hoops Have Unique Halving》
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作者：
Rob Arthan, Paulo Oliva
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最新提交年份：
2013
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分类信息：

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：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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英文摘要：
  Continuous logic extends the multi-valued Lukasiewicz logic by adding a halving operator on propositions. This extension is designed to give a more satisfactory model theory for continuous structures. The semantics of these logics can be given using specialisations of algebraic structures known as hoops. As part of an investigation into the metatheory of propositional continuous logic, we were indebted to Prover9 for finding a proof of an important algebraic law.
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PDF链接：
https://arxiv.org/pdf/1203.0436