Concurrency Theory and Non-Numerical Approximation

并行系统和近似问题在人类的经验中大量存在，但它们的充分的概念化尚未得到我们的理解。我们在管理和控制人类事务和活动方面日益依赖于越来越复杂的系统，这增加了发展更充分和更可取的更正式的概念以保持对我们所创造的系统的可靠控制的紧迫性。****正确规范设计和验证其行为的问题的解决变得至关重要，一个令人满意的严格规范和验证的概念装置变得必不可少。****该项目将探讨有关并行系统和近似推理的形式推理的理论问题。第一个总体目标是开发一个框架，基于离散关系结构（由Janicki和Koutny开发）建模的广义因果关系概念和Mazurkiewicz轨迹的泛化，以支持复杂并发系统的设计和验证。第二个总体目标是加强基础和改进非数值近似和非数值排序技术的应用。****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.**