摘要翻译：
在这本书中，我们考虑了各种多值逻辑：标准的，线性的，双曲的，抛物线的，非阿基米德的，p-adic的，区间的，中性的，等等。我们还考察了结果，这些结果显示了多值逻辑的不同证明理论框架，例如以下演绎演算的框架：希尔伯特的风格，序贯和超序贯。我们提出了一种通用的方法，它允许为一大族非阿基米德多值逻辑构造系统的解析演算：超有理值、超实值和p-adic值逻辑，这些逻辑以一种特殊的语义格式为特征，适当地拒绝阿基米德公理。这些逻辑是作为标准多值逻辑（即Lukasiewicz逻辑、Goedel逻辑、Product逻辑和Post逻辑）的不同扩展而构建的。阿基米德公理的非正式意义是，任何东西都可以用尺子测量。此外，没有阿基米德公理的逻辑多重有效性在于真值集是无限的，它不是有根据的和有序的。在非阿基米德值逻辑的基础上，我们构造了非阿基米德值区间中性逻辑INL，并用它来描述中性现象。
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英文标题：
《Neutrality and Many-Valued Logics》
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作者：
Andrew Schumann, Florentin Smarandache
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最新提交年份：
2007
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分类信息：

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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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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英文摘要：
  In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.
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PDF链接：
https://arxiv.org/pdf/0707.3205