An adjoint functors approach to models of cognition

2019 Fiscal Year Final Research Report

• Project/Area Number: 16KT0025
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Multi-year Fund
• Section: 特設分野
• Research Field: Mathematical Sciences in Search of New Cooperation
• Research Institution: National Institute of Advanced Industrial Science and Technology
• Principal Investigator: Phillips Steven 国立研究開発法人産業技術総合研究所, 情報・人間工学領域, 上級主任研究員 (90344209)
• Co-Investigator(Kenkyū-buntansha): 武田 裕司 国立研究開発法人産業技術総合研究所, 情報・人間工学領域, 研究チーム長 (10357410)
• Project Period (FY): 2016-07-19 – 2020-03-31
• Keywords: 圏論 / 普遍的構造 / システム性 / 学習 / 刺激‐反応

Outline of Final Research Achievements

Dual-process theories are controversial because they are vaguely defined and don’t always align with the supposed distinctions. We proposed a category theory (adjoint functors) approach to dual-process aspects of cognition. A series of experiments were conducted to elicit dual-processing routes within a given task. Our main theoretical result was to show that an associative/relational (rule-based) form of dual-process is related by a category (sheaf) theory construction, called sheaving, which is an adjoint functor. This result provides a new way of modeling cognitive representations and processes.

Free Research Field

Cognitive Science

Academic Significance and Societal Importance of the Research Achievements

Human cognition involves two different styles of thinking: fast, reflexive and effortless (Type 1) versus slow, reflective and effortful (Type 2). The challenge is to provide a coherent theoretical account of the apparent dual nature of cognition.