鹿島 亮 （かしま りょう）

研究テーマ

• 数理論理学．特に非古典論理やラムダ計算の証明論的研究．

主要論文

• 鹿島 亮: 到達可能関係の推移閉包を扱う様相論理のカノニカルモデルについて, 京大数理解析研究所講究録 1729 pp.36-47 (2011).
• Ryo Kashima: Completeness proof by semantic diagrams for transitive closure of accessibility relation, Advances in Modal Logic, Volume 8, pp. 200-217 (2010).
• Ryo Kashima: A proof of the completeness theorem for the modal logic with transitive closure of accessibility relation, Research Reports on Mathematical and Computing Sciences, C-266, (Tokyo Institute of Technology, 2009). pdf file
• Ryo Kashima and Keishi Okamoto: General Models and Completeness of First-Order Modal mu-calculus, Journal of Logic and Computation 18[4], pp.497-507 (2008).
• Ryo Ishigaki and Ryo Kashima: Sequent Calculi for Some Strict Implication Logics, Logic Journal of the IGPL 16[2], pp.155-174 (2008).
• Ryo Kashima and Keishi Okamoto: Completeness Theorem of First-Order Modal mu-calculus, Research Reports on Mathematical and Computing Sciences, C-244, (Tokyo Institute of Technology, 2007). pdf file
• 鹿島 亮: 中間述語論理CDについて, 京大数理解析研究所講究録 1533 pp.1-8 (2007). pdf file
• Ichiro Hasuo and Ryo Kashima: Kripke Completeness of First-Order Constructive Logics with Strong Negation, Logic Journal of the Interest Group in Pure and Applied Logics 11[6], pp.615-646 (2003).
• Katsumasa Ishii, Ryo Kashima, and Kentaro Kikuchi: Sequent Calculi for Visser's Propositional Logics, Notre Dame Journal of Formal Logic 42[1], 1-22 (2001) (published 2003).
• Ryo Kashima: On Semilattice Relevant Logics, Mathematical Logic Quarterly 49[4], 401-414 (2003).
• Ryo Kashima: Proof Theoretical Studies on Semilattice Relevant Logics, Research Reports on Mathematical and Computing Sciences, C-157, (Tokyo Institute of Technology, 2001). pdf file
• Ryo Kashima: On the Standardization Theorem for Lambda-Beta-Eta-Calculus, International Workshop on Rewriting in Proof and Computation (RPC'01), (Sendai, Japan. October 2001). pdf file
• Ryo Kashima: Completeness of Implicational Relevant Logics, Logic Journal of the Interest Group in Pure and Applied Logics 8, pp.761-785 (2000).
• Ryo Kashima: A Proof of the Standardization Theorem in Lambda-Calculus, Research Reports on Mathematical and Computing Sciences, C-145, (Tokyo Institute of Technology, 2000). pdf file
• Ryo Kashima: Labelled sequent calculi and completeness theorems for implicational relevant logics, Research Reports on Mathematical and Computing Sciences, C-140, (Tokyo Institute of Technology, 1999). pdf file
• 鹿島 亮: 非古典論理のシーケント計算 --- 完全性定理のシーケント計算による証明, 日本数学会 数学基礎論分科会 1999年度年会 特別講演 (アブストラクト集 pp.49-67). pdf file
• Ryo Kashima and Norihiro Kamide: Substructural Implicational Logics Including the Relevant Logic E, Studia Logica 63 pp.181-212 (1999).
• Ryo Kashima and Takeshi Yamaguchi: On the Difficulty of Writing Out Formal Proofs in Arithmetic, Mathematical Logic Quarterly 43 pp.328-332 (1997).
• Ryo Kashima: Contraction-Elimination for Implicational Logics, Annals of Pure and Applied Logic 84, pp.17-39, (1997).
• Ryo Kashima: Cut-Free Sequent Calculi for Some Tense Logics, Studia Logica 53 pp.119-135 (1994).
• Ryo Kashima and Tatsuya Shimura: Cut-Elimination Theorem for the Logic of Constant Domains, Mathematical Logic Quarterly 40 pp.153-172 (1994).
• Ryo Kashima and Yuichi Komori: The Word Problem for Free BCI-Algebras Is Decidable, Mathematica Japonica 37 No.6 pp.1025-1029 (1992).
• Ryo Kashima: Cut-Elimination Theorem for the Intermediate Logic CD, Research Reports on Mathematical and Computing Sciences, C-100, (Tokyo Institute of Technology, 1991). pdf file

著書・訳書

• 鹿島亮 著： 数理論理学, 朝倉書店(2009). (正誤表)
• 鹿島亮 著： C言語による 計算の理論, サイエンス社(2008). (正誤表)
• 田中一之・鹿島亮・山崎武・白旗優 共著： ゲーデルと20世紀の論理学・第3巻・不完全性定理と算術の体系, 東京大学出版会(2007).
• 田中一之・鹿島亮・角田法也・菊池誠 共著： 数学基礎論講義 ―― 不完全性定理とその発展, 日本評論社(1997).
• M.ジャキント 著, 確かさを求めて, 培風館(2007)（共訳）.