1997 Fiscal Year Final Research Report Summary
A funtadamental study on graph transforamtion systems with relational calculus
| Project/Area Number |
07680363
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | KYUSHU UNIVERSITY |
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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)
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| Co-Investigator(Kenkyū-buntansha) |
OHSUKA Hiroshi Kyushu University, Department of Mathematics, Lecturer, 大学院・数理学研究科, 講師 (30203839)
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| Project Period (FY) |
1995 – 1997
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| Keywords | graph transformation / graph grammar / relational calculus / relation algebra / category theory / fuzzy set / fuzzy relation / fuzzy graph |
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| 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.
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