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Higher Order Unification and Mechanization of Higher Order Theorem Proving System

Research Project

Project/Area Number 01580020
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Informatics
Research InstitutionKyushu Institute of Technology

Principal Investigator

HARAO Masateru  KIT, Fac. of CSSE Professor, 情報工学部, 教授 (00006272)

Co-Investigator(Kenkyū-buntansha) FUJITA Kenetsu  KIT, Fac. of CSSE Assistant, 情報工学部, 助手 (30228994)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
KeywordsHigher order logic / lambda-calculus / Higher order unification / Theorem proving / Mechanization of Proving system / Logic language / Analogical reasoning / Inference mechanism / 型理論 / マッチング / 計算の複雑さ / 導出原理 / 人工知能
Research Abstract

We have studied in this year by setting the following themes : (1) Formalization of higher order logic language based on lambda-logic, (2) Design of higher order unification algorithm for mechanizing theorem proving system, (3) Higher order inference system for knowledge processings.
For the theme (1), we designed a higher order program language by extending the Horn clause to a higher order case, and some results have been obtained. For the theme (2), a new class of higher order language in which the unification algorithm becomes computable has been made clear. Especially computational complexity of unification algorithm for 2nd order terms has been discussed precisely. For (3), we have demonstrated that a kind of analogical reasoning system can be realized in the framework of proposed higher order language, and it is ascertained that the proposed method is available for designing intelligent knowledge processing system.

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] 原尾,岩沼: "高階ユニフィケ-ションにおける可解なクラスと計算の複雑さ" LAシンポシウム,京都大学数理解研講究録. No.7.31. 37-48 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 岩沼,原尾: "非再帰的な述語サ-カムスクリプションの一階論理式への等価変換" 人工知能学会論文誌. Vol.5 No.4. 462-470 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Harao: "Analogical Reasoning Based on Higher Order Unification" First International Conference on Algorithmic Learning Theory,. Proceeding. 151-163 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K.Iwanuma,M.Harao,S.Noguchi: "Reconsideration of Pointwise Circumscription,Transformation of Non‐Recursive Predicate Circumscription into First‐Order Sentences" International eonference on Info.Japan. 351-356 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K.Fujita,A.Togashi,S.Noguchi: "A Canonical Translation from Higner Order Logic to Typed Lambda Calculus." 人工知能学会誌. Vol.5 No.6. 796-807 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 原尾,岩沼: "高階項マッチングアルゴリズムの計算複雑さについて" 日本ソフトウェア科学会論文誌. Vol.8 No.1. 41-53 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Harao, K. Iwanuma: "Solvable class and computational complexity of higher order unification" Proc. of LA symposium LN of Kyoto Univ.No. 731. 37-48 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Harao, K. Iwanuma: "An Equivalent Transformation of Non-Recursive Predicate Circumscription to First-Order Formulas" J. of JSAI. vol. 5, No. 4. 462-470 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Harao: "Analogical Reasoning Based on Higher Order Unification" Proc. of First International Conf. on Algorithmic Learning Theory. 151-163 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Iwanuma, M. Harao, S. Noguchi: "Reconsideration of Point wise Circumscription of Non-Recursive Predicate Circumscription into First Order Sentences," Proc. of International Conf. on Information Japan. 351-356 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Fujita, A. Togashi, S. Noguchi: "A Canonical Translation from Higher Order Logic to Typed Lambda Calculus" J. of JSAI. vol. 5, No. 6. 796-807 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] M. Harao, K. Iwanuma: "Computational Complexity of Higher Order Matching Algorithm" J. of Computer Software. vol. 8, No. 1. 41-53 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 原尾,岩沼: "高階ユニフィケ-ションにおける可解なクラスと計算の複雑さ" LAシンポシウム,京都大学数理解研講究録. No.731. 37-48 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 岩沼,原尾: "非再帰的な述語サ-カムスクリプションの一階論理式への等価変換" 人工知能学会論文誌. Vol.5 No.4. 462-470 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Harao: "Analogical Reasoning Based on Higher Order Unification" First International Conference on Algorithmic Learning Theory. Proceeding. 151-163 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.Iwanuma,M.Harao,S.Noguchi: "Reconsideration of Pointwise Circumscription,Transformation of NonーRecursive Predicate Circumscription into FirstーOrder Sentences" International Conferecnce on Info.Japan. Proceeding. 351-356 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.Fujita,A.Togashi,S.Noguchi: "A Canonical Translation from Higher Order Logic to Typed Lambda Calculus" 人工知能学会誌. Vol.5 No.6. 796-807 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 原尾,岩沼: "高階項マッチングアルゴリズムの計算複雑さについて" 日本ソフトウェア科学会論文誌. Vol.8 No.1. 41-53 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 安孫子,原尾,岩沼: "高階論理ユニフィケ-ションを用いた知識処理" 京都大学数解研 講究録. No.695. 89-107 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 原尾,岩沼: "定理証明的手法による再帰方程式から回路の自動設計" 電子情報通信学会論文誌. Vol.J72-D-II、No.5. 772-781 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 原尾: "高階ユニフィケ-ションに基づく知識処理" 人工知能基礎論研究会. ,SIG-FAI-8903-3. 21-30 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 原尾,岩沼: "高階ユニフィケ-ションにおけ可解なクラスと計算の複雑さ" 京都大学数理解析研アルゴリズムと計算量の理論研究集会. (1990)

    • Related Report
      1989 Annual Research Report
  • [Publications] 原尾,岩沼: "高階ユニフィケ-ションの計算複雑さ"

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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