Project/Area Number  02452010 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Kyushu University 
Principal Investigator 
TANAKA Syunichi Kyushu Univ., Faculty of Sci., Professor, 理学部, 教授 (00028127)

CoInvestigator(Kenkyūbuntansha) 
山本 野人 九州大学, 理学部, 助手 (30210545)
OHTSUKA Hiroshi Kyushu Univ., Faculty of Sci., Assistant, 理学部, 助手 (30203839)
YANAGAWA Takashi Kyushu Univ., Faculty of Sci., Associate Professor, 理学部, 助教授 (80029488)
NAKAO Mitsuhiro Kyushu Univ., Faculty of Sci., Associate Professor, 理学部, 助教授 (10136418)
河原 康雄 九州大学, 理学部, 助教授 (90091181)
KAWASAKI Hidefumi Kyushu Univ., Faculty of Sci., Lecturer, 理学部, 講師 (90161306)
FURUKAWA Nagata Kyushu Univ., Faculty of Sci., Professor, 理学部, 教授 (50037165)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥6,400,000 (Direct Cost : ¥6,400,000)
Fiscal Year 1991 : ¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1990 : ¥3,800,000 (Direct Cost : ¥3,800,000)

Keywords  Complex Systems / Formal Methods / Axiomatic Set Theory / Concurrency / Nonstandard Analysis / 複雑システム / 形式的方法 / 公理的集合論 / 並行性 / 超準解析 / 並行プロセス / 述語論理 
Research Abstract 
The purpose of this project is to study possible relations between computing science and complex systems such as brain and market. As yet no secure theoretical foundation for studying these systems is available, we tried to search the one. The candidate is Formal Mathematics and Science based on the axiomatic set theory. Nonstandard Analysis is an important example in mathematics. In information and languages, Milner's Process Calculus and Barwise's Situation Theory (for natural languages) are formalized on nonwellfounded set theory (developed by Aczel). These independent developments suggest the unity of various formal methods. Neural network theory is a dynamical aspects of a complex system. Infinitesimals and hyperfinite integers of nonstandard analysis may give us new perspective on large finite dynamical systems. Details of above observations are contained in the accompanying report.
