Proof-Theoretic Study of Doxastic and Epistemic Updates via Questions

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K12113
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: Hokkaido University
• Principal Investigator: Sano Katsuhiko 北海道大学, 文学研究院, 教授 (20456809)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 認識論理 / 信念の論理 / 疑問文 / 動的認識論理 / 証明論 / 分散知識

Outline of Final Research Achievements

This study examines how agents update their knowledge and beliefs through inquiries (i.e., making questions) in situations where complete information is not available. We do this from the perspective of proof theory, in particular a sequent calculus whose unit of inference is a consequence relation. To handle questions, we developed a proof theory for a fragment of a first-order expansion of inquisitive logic, which treats both interrogative and declarative sentences within the same framework. We have established proof theories for epistemic logic on intuitionistic logic and its dynamic expansions to address reasoning under incomplete information. In particular, we focused on the concept of distributed knowledge concerning the combination of knowledge among multiple agents.

Free Research Field

論理学

Academic Significance and Societal Importance of the Research Achievements

本研究は、不完全情報下で「なぜ」「どうして」といった質疑によってエージェントの知識・信念の更新がどのようになされるかを、疑問文を伴う推論の側面から証明論的に探究し、環境から情報を手に入れながら自律的に動作するロボットの制御、質問により嘘・矛盾を見抜く対話システムの設計に、論理的基盤を与えることに貢献しうる。証明論的手法は、環境について部分的情報しか知り得ない不完全情報下では、モデルの完全記述が必要なモデル理論的手法より利点がある。