Concurrency Theory and Non-Numerical Approximation

并发系统和近似问题在人类经验中比比皆是，但它们的完全适当的概念化尚未摆脱我们。在管理和控制人类事务和活动时，我们越来越依赖于越来越复杂的系统，这就增加了开发更适当、更可取、更正式的概念的紧迫性，以保持对我们所创建的系统的可靠控制。解决设计的正确规范和验证其行为的问题变得至关重要，并且严格规范和验证的令人满意的概念装置变得至关重要。该项目将探讨并发系统和近似推理的形式化推理所涉及的理论问题。第一个总体目标是开发一个框架，基于离散关系结构（Janicki和Koutny开发的）和Mazurkiewicz轨迹的泛化建模的广义因果关系的概念，以支持复杂的并发系统的设计和验证。第二个总目标是加强非数值近似和非数值排序技术的基础和改进其应用。连接这三个主题的是方法论，因为科学方法基本上是相同的，即，离散数学，特别是集合、关系和自动机理论，当然还有形式逻辑。

Both concurrent systems and approximation problems abound in human experience but their fully adequate conceptualization as yet eludes us. Our increasing dependence on ever more complex systems in the management and control of human affairs and activities increases the urgency for developing more adequate and preferable more formal concepts to maintain reliable control over systems we have created.****The solution of the problem of correct specification of the design and verification of its behaviour becomes crucial, and a satisfactory conceptual apparatus for rigorous specification and verification becomes essential.****The project will explore theoretical issues involved in the formal reasoning about concurrent systems and approximate reasoning. First general aim is to develop a framework, based on the concept of Generalized Causality modelled by Discrete Relational Structures (developed by Janicki and Koutny) and generalization of Mazurkiewicz traces, to support the design and the verification of sophisticated concurrent systems. The second general aim is to strengthen foundations and improve applications of non-numerical approximation and non-numerical ranking techniques.****What connects all three topics is methodology, as the scientific method is basically the same, i.e., discrete mathematics, especially set, relation and automata theory and of course formal logic.**