可计算性逻辑中的切换运算符

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摘要翻译：
可计算性逻辑(CL)（见http://www.cis.upen.edu/~giorgi/CL.html)是一个研究程序，旨在将逻辑重新发展为可计算性的形式理论，而不是传统上的真的形式理论。CL中的公式代表交互式计算问题，被视为机器与其环境之间的博弈；逻辑运算符表示对这类实体的操作；而“真理”被理解为存在一个有效的解决方案。语言学习的形式主义是开放的，随着学科研究的深入，它可能会经历一系列的扩展。到目前为止，人们已经研究了三种合取方式--平行式、顺序式和选择式。本论文在这个集合中增加了一个更自然的种类，称为拨动。切换操作可以被描述为选择操作的宽松版本，其中选择是可伸缩的，允许被重新考虑任何有限次。通过这种方式，他们在交互式计算中对试错式决策步骤进行建模。本文的主要技术成果是为可计算逻辑的命题片段构造了一个完整的公理化，它的词汇和否定一起包含了并行、切换、顺序和选择四种合取。除了切换合取之外，本文还介绍了量词的切换版本和递归操作。
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英文标题：
《Toggling operators in computability logic》
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作者：
Giorgi Japaridze
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最新提交年份：
2010
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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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英文摘要：
  Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been. Formulas in CL stand for interactive computational problems, seen as games between a machine and its environment; logical operators represent operations on such entities; and "truth" is understood as existence of an effective solution. The formalism of CL is open-ended, and may undergo series of extensions as the studies of the subject advance. So far three -- parallel, sequential and choice -- sorts of conjunction and disjunction have been studied. The present paper adds one more natural kind to this collection, termed toggling. The toggling operations can be characterized as lenient versions of choice operations where choices are retractable, being allowed to be reconsidered any finite number of times. This way, they model trial-and-error style decision steps in interactive computation. The main technical result of this paper is constructing a sound and complete axiomatization for the propositional fragment of computability logic whose vocabulary, together with negation, includes all four -- parallel, toggling, sequential and choice -- kinds of conjunction and disjunction. Along with toggling conjunction and disjunction, the paper also introduces the toggling versions of quantifiers and recurrence operations.
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PDF链接：
https://arxiv.org/pdf/0904.3469

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