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.

该项目是从跨学科的观点组织进行分类计算机数学投资的。与该研究项目一起加入的所有研究人员都研究了理论ﾟ COF类别，Dedekind类别，最终核，二维射击小队同步，证明和类型的理论，完整性，象征性和计算逻辑的完整性，符号和计算逻辑，归纳性的归纳性，直觉和典型的典范和典型的自然范围，审查和典型的自然推论，逐渐验证，并进行了批评，并进行了批评，并进行了批评，并进行了批评规则，典型的规则，定制，规则，典型的典范线程，与类别理论的数学有关。作为研究项目的结果，我们在日本广泛开发了计算机数学，也就是说，我们给出了许多有用的应用数学的新理论，证明了逻辑理论，类别理论，自动机理论和人工智能的新理论，并最终提出了当代数学的新趋势。 1996年，1997年12月和1998年12月。（该联合会议的历史相当长，大约三十年。）该研究项目的详细摘要在1999年3月在京都大学的Informatatics的报告（小册子）报告中进行了描述。校长调查员，代表该项目的调查员，以提供资金支持。