Computing Science and Complex systems

该项目的目的是研究计算科学与大脑和市场等复杂系统之间可能存在的关系。由于研究这些系统还没有可靠的理论基础，我们试图寻找一个。候选人是形式数学和科学的基础上公理集理论。非标准分析是数学中的一个重要例子。在信息和语言中，米尔纳的过程演算和巴怀斯的情境理论（用于自然语言）是在非良基集合论（由Aczel开发）上形式化的。这些独立的发展表明了各种形式化方法的统一性。神经网络理论是复杂系统的动力学方面。非标准分析中的无穷小和超有限整数可能给我们研究大型有限动力系统提供新的视角。上述观察的细节包含在随附的报告中。

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 non-well-founded 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.