摘要翻译：
可计算性逻辑(CL)（见http://www.cis.upenn.edu/~giorgi/CL.html)是最近推出的一个程序，旨在将逻辑重新发展为可计算性的形式理论，而不是逻辑传统上所说的真的形式理论。其中的公式代表计算问题，“真”意味着算法解的存在，而证明则编码了这种解。在为CL的更多表达片段寻找公理化的研究中，本文引入了一个新的演绎系统CL12，并证明了它在CL语义方面的合理性和完备性。保守地扩展了经典谓词演算，并提供了相当多的额外的表达和演绎能力，CL12提出了一个合理的，计算上有意义的，建设性的替代经典逻辑作为应用理论的基础。本文将传统的基于经典逻辑的Peano算法重建为基于可计算逻辑的Peano算法，以获得此类理论的一个模型实例。本文的目的之一是提供一个起点，如作者所希望的那样，可能成为一个具有有趣发现潜力的新的研究路线--探索基于CL的算术和其他基于CL的应用系统的可能相当不寻常的元理论。
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英文标题：
《Towards applied theories based on computability logic》
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作者：
Giorgi Japaridze
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最新提交年份：
2009
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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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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：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
  Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting findings -- an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems.
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PDF链接：
https://arxiv.org/pdf/0805.3521