A proof-theoretical investigation on diagrammatic reasoning

图解推理的证明理论研究

• 批准号: 22820053
• 负责人: TAKEMURA Ryo
• 金额: $ 1.9万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-22820053/
• 关键词: 論理学; 証明論; 図形推論

Recently, logical reasoning based on diagrammatic or graphical representations has been investigated by researchers from various areas. For the study of diagrammatic reasoning, it is important to combine methods and analyses of traditional symbolic logic and cognitive science. In such studies, researches so far have concentrated on semantic studies on the static nature of diagrams, i. e., the nature at the level of representation. And there are few proof-theoretical investigations on the dynamic nature of diagrams, i. e., the nature at the level of proofs or at the level of manipulation of diagrams.In this study, I introduced a proof-theoretical framework to investigate the dynamic nature of diagrammatic representations, in particular of Euler and Venn diagrams. Then, I formalized, by applying one of the basic proof-theoretical techniques of logic translation, the notion of "free ride" in my proof-theoretical framework. Free ride is one of the most basic properties of diagrams that is mainly discussed in the literature of cognitive science as an account of inferential efficacy of diagrams. Then, based on the formalization of free ride, I investigated a proof-theoretical characterization of the structure of Euler diagrammatic proofs and that of Venn diagrammatic proofs, compared with the usual natural deduction proofs of the traditional symbolic logic.

最近，逻辑推理的基础上图表或图形表示已被研究人员从各个领域。对于图形推理的研究，应将传统符号逻辑和认知科学的方法和分析联合收割机结合起来。在这类研究中，迄今为止的研究主要集中在对图的静态性质的语义研究，即对图的静态性质的语义研究。例如，代表性层面的性质。而关于图的动态性质的证明理论研究很少，即：例如，在这项研究中，我引入了一个证明理论框架来研究图形表示的动态性质，特别是欧拉图和维恩图。然后，我形式化，通过应用逻辑翻译的基本证明理论技术之一，在我的证明理论框架中的“搭便车”的概念。搭便车是图的一个最基本的性质，在认知科学的文献中主要讨论的是图的推理效能。然后，在搭便车形式化的基础上，与传统符号逻辑中通常的自然演绎证明进行比较，研究了欧拉图证明和维恩图证明结构的证明论特征。

项目成果

オイラー図推論の証明論的分析:自然演繹への翻訳と正規形証明

欧拉图推理的证明分析：转化为自然演绎和范式证明

• 发表时间: 2011
• 作者: Suzuki;M.;竹村亮
• 通讯作者: 竹村亮

オイラー図推論の証明論的分析:Free ride propertyと正規形証明

欧拉图推理的证明分析：搭便车性质与范式证明

• 发表时间: 2010
• 作者: Nakamura;F.;Suzuki;M.;Kohbara;A. & Sakai;K;竹村亮
• 通讯作者: 竹村亮

A diagrammatic inference system with Euler circles

具有欧拉圆的图解推理系统

• 期刊: Journal of Logic, Language and Information
• 作者: Koji Mineshima;Mitsuhiro Okada;Ryo Takemura
• 通讯作者: Ryo Takemura

Proof theory for reasoning with Euler diagrams : a Logic Translation and Normalization

用欧拉图推理的证明理论：逻辑转换和规范化

• DOI: 10.1007/s11225-012-9370-6
• 发表时间: 2012
• 期刊: Studia Logica
• 影响因子: 0.7
• 作者: Nakanishi;H.;Ryo Takemura
• 通讯作者: Ryo Takemura

A Diagrammatic Reasoning System with Euler Circles

欧拉圆图解推理系统

• 发表时间: 2011
• 期刊: Journal of Logic, Language and Information
• 作者: Koji Mineshima;Mitsuhiro Okada;Ryo Takemura
• 通讯作者: Ryo Takemura