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A funtadamental study on graph transforamtion systems with relational calculus

Research Project

Project/Area Number 07680363
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

KAWAHARA Yasuo  Kyushu University, Department of Informatics, Professor, 大学院・システム情報科学研究科, 教授 (90091181)

Co-Investigator(Kenkyū-buntansha) OHSUKA Hiroshi  Kyushu University, Department of Mathematics, Lecturer, 大学院・数理学研究科, 講師 (30203839)
Project Period (FY) 1995 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1997: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1995: ¥700,000 (Direct Cost: ¥700,000)
Keywordsgraph transformation / graph grammar / relational calculus / relation algebra / category theory / fuzzy set / fuzzy relation / fuzzy graph / 関係代数 / ファジィ集合 / ファジィ関係 / ファジィグラフ
Research Abstract

This reseach project obtained the following results :
・We developed an axiomatic formalisation of fuzzy relation algebras as a foundation of fuzzy relational calculus. By using the formalisation we generalized the representation problem for relation algebras, due to A.Tarski, to a representation problem for Dedekind and Zadeh categories, and we gave proofs of the representation problem for Dedekind and Zadeh categories.
・We proposed a new matching method for fuzzy graphs in a theory of fuzzy graph transformations based on fuzzy relational calculus. Then we proved the existence of pullbacks in a category of fuzzy graphs, which gurantees the foundation for pullback graph transformations.
・We invented relational set theory as an important foundation for graph transformations as well as mathematics and theoretical computer science. Also, we investigated its applications from a quite wide view.
・The detailed summary of this reseach project is described in the report of the reseach project (booklet), printed in Department of Informatics, Kyushu University. The head investigator, on behalf of investigators of the project, is grateful for giving the financial suport.

Report

(4 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • 1995 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Y.Kawahara: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara: "A small final coalgebra theorem" To appear in Theoretical Computer science.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Mori: "Rewriting fuzzy graphs" DOI Technical Report DOI-TR-CS,Kyushu University. 132. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara: "Crispness and representation theorem in Dedekind categories" 京都大学数理解析研究所講究録. 1021. 63-69 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.kawahara: "Relational set theory" Lecture Notes in Computer Science. 953. 44-58 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Y.Lee and Y.Kawahara: "Transition diagrams of finite cellular automata" Bull.Inform.Cybernet.28. 47-69 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.Inokuchi, T.Sato, A.hara, S.Kumamoto, H.-Y.Lee and Y.Kawahara: "Computational analysis of cellular automata with triplet transition rule." Research Report on Information Science and Electical Engineering of Kyushu University. 1(1). 79-84 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara and H.Y.Lee: "Period lengths of cellular automata cam-90 with memory" Journal of Mathematical Physics. 38(1). 255-266 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara and H.Furusawa: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara and M.Mori: "A small final coalgebra theorem." To appear in Theoritical Computer Science. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara, H.Furusawa and M.Mori: "Categorical representation theorems of fuzzy relations." The Proceeding of 4th International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD'96). 190-197 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] M.Mori and Y.Kawahara: "Rewriting fuzzy graphs." DOI Technical Report DOI-TR-CS 132, Department of Informatics, Kyushu University.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara and H.Furusawa: "Crispness and representation theorem in Dedekind categories." DOI Technical Report DOI-TR-CS 143, Department of Informatics, Kyushu University.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Y.Kawahara: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Kawahara: "A small final coalgebra theorem" To appear in Theoretical Computer Science.

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Mori: "Rewriting fuzzy graphs" DOI Technical Report DOI-TR-CS,Kyushu University. 132. (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y.Kawahara: "Crispness and representation theorem in Dedekind categorecs" 京都大学数理解析研究所構究録. 1021. 63-69 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Y.Lee: "Transition diagrams of finite cellular automata" Bull.Inform.Cybernet.28. 47-69 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] S.Inokuchi: "Computational analysis of cellular automata with triplet transition rule" Research Report on Info.Sci.and Elect.Eng.of Kyushu University. 28. 79-84 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Kawahara: "Period lengths of cellular automata cam-90 with memory" Journal of Mathematical Physics. 38. 255-266 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Kawahara: "Categorical representation theorems of fuzzy relations" DOI Technical Report DOI-TR-CS 124,Kyushu Univ.(1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Kawahara: "An algebraic formalization of fuzzy relations" To appear in International Journal for Fuzzy Sets and Systems.

    • Related Report
      1996 Annual Research Report
  • [Publications] Y. Kawahara: "Period lengths of cellular automata on square lattices with rule 90" Journal of Mathematical Physics. 36. 1435-1456 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Y. Kawahara: "Relational graph rewritings" Theoretical Computer Science. 141. 311-328 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Y. Kawahara: "Relational set theory" Lecture Notes in Computer Science. 953. 44-58 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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