A logical investigation of diagrammatic reasoning and non-deductive reasoning based on linear logic

2015 Fiscal Year Final Research Report

• Project/Area Number: 24720016
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Philosophy/Ethics
• Research Institution: Nihon University
• Principal Investigator: TAKEMURA Ryo 日本大学, 商学部, 准教授 (70583665)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 論理学 / 証明論 / 線形論理 / 図形推論

Outline of Final Research Achievements

In the traditional logic, deductive reasoning based on the sentential/symbolic representation has been studied. By extending the framework of the traditional logic, I investigated reasoning based on diagrammatic/graphical representations and on non-monotonic and non-deductive inference rules.
I investigated, as case studies on diagrammatic reasoning, reasoning based on Euler diagrams, Venn diagrams, correspondence tables, and mathematical graphs. I further investigated heterogeneous reasoning combining these diagrams and sentential representation.
I investigated non-monotonic reasoning in terms of linear logic. I further studied one of the major non-deductive reasoning called abduction. Furthermore, I tried to apply my results on diagrammatic and non-deductive reasoning to teaching logic and mathematics.

Free Research Field

論理学