Interdisciplinary study on logic, with a special focus on intuitionistic logic

2017 Fiscal Year Final Research Report

• Project/Area Number: 26284005
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Philosophy/Ethics
• Research Institution: Keio University
• Principal Investigator: Okada Mitsuhiro 慶應義塾大学, 文学部(三田), 教授 (30224025)
• Co-Investigator(Kenkyū-buntansha): 金子 洋之 専修大学, 文学部, 教授 (60191988) ; 峯島 宏次 お茶の水女子大学, シミュレーション科学教育研究センター, 特任講師 (80725739)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 論理と数学の哲学 / 図形推論 / 直観主義論理 / 証明論 / Wittgenstein哲学 / 日常推論の認知科学 / フッサール論理学 / 情報論理

Outline of Final Research Achievements

We analyzed Husserl's theory of constructible definite manifolds and Wittgenstein's theory of inductive proofs from the constructivist philosophy of mathematics. We developed a Fitting-forcing-based classical model construction method from intuitionistic possible world semantics for introducing a new semantics with computational interpretations. We gave a concrete application of this semantics to the computer security field. We also developed a general theory of proof normalization in an abstruct setting. We also developed some new proof-theoreric methods for analizing diagrammatic logic. We introduced various experimental methods in our research to consider the process models of logical inferences in our ordinary life. Our methods include cognitive scientific/cognitive psychological, behavioral genetic psychological, social psychological methods and others.

Free Research Field

論理学