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An interdisciplinary study on categorical computer mathematics

分类计算机数学的跨学科研究

基本信息

批准号：
08304017
负责人：
KAWAHARA Yasuo
金额：
$ 6.08万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

This project was organized for investigations on categorical computer mathematics from inter-disciplinary viewpoints. All the investigators joining with this research project studied theoryﾟCof categories, Dedekind categories, final coalgebras, two-dimensional firing squad synchro-nization, proof and type theories, completeness for uniformly delayed circuits, symbolic and computational logics, inductive inference of real functions, intuitionistic and classical natural deduction systems with catch and throw rules, testing proofs by examples, and an approximation of protein threading, concerned with mathematics of category theory. As the results of the research projects we extensively developed computer mathematics in Japan, that is, we gave a lot of new theories of useful applied mathematics, proved new theorems in logic, category theory, automata theory, and artificial intelligence, and finally suggested new trends of contemporary applied mathematics.Also the head investigator organized the Japanese joint conferences of applied mathematics at Ryukoku University, Seta City in December 1996, December 1997 and December 1998. (This joint conference has rather long history about thirty years long.) The detailed summary of this research project is described in the report of the research project (booklet), printed in Department of Informatics, Kyushu University, March 1999. The head investigator, on behalf of investigators of the project, is grateful for giving the financial support.

本项目旨在从跨学科的角度对分类计算机数学进行研究。本课题研究人员主要研究了范畴理论、Dedekind范畴、最终共代数、二维射击队同步、证明与类型论、一致延迟电路的完备性、符号逻辑与计算逻辑、实函数的归纳推理、带有接掷规则的直觉与经典自然演绎系统、实例检验证明、蛋白质穿线近似。关于范畴论的数学。作为研究项目的成果，我们在日本广泛发展了计算机数学，即提出了许多有用的应用数学的新理论，证明了逻辑学、范畴论、自动机论、人工智能等方面的新定理，并提出了当代应用数学的新趋势。此外，首席研究员于1996年12月、1997年12月和1998年12月在濑田市的琉球大学组织了日本应用数学联合会议。（这个联席会议有相当长的历史，大约有30年之久。）九州大学信息系1999年3月出版的《研究项目报告（小册子）》中详细介绍了本研究项目的概况。首席研究员代表该项目的研究人员，对给予的财政支持表示感谢。