Concurrency and Approximate Reasoning

该项目涉及两个主题，第一个涉及并发性，第二个是近似推理。 并行系统丰富了人类的经验，但它们的充分概念化至今仍不为我们所知。我们在管理和控制人类事务和活动方面越来越依赖越来越复杂的系统，因此迫切需要制定更充分、更可取的更正式的概念，以维持对我们创建的系统的可靠控制。 解决正确规范设计和验证其行为的问题变得至关重要，而一个令人满意的严格规范和验证的概念性设备变得至关重要。该项目将探索关于并发系统和近似推理的形式推理所涉及的理论问题。我们的总体目标是基于由离散关系结构建模的广义因果关系和广义踪迹的概念(均由Janicki和Koutny提出)来开发一个框架，以支持复杂并发系统的设计和验证。 当经验数据被表示为一些形式结构时，结果可能不具有所有必需的性质。例如，任何排序关系至少应该是偏序，但通过各种主观判断获得的关系可能包含循环。问题是如何找到具有特定性质的结构对给定结构的最佳逼近。虽然粗糙集很好地处理了下近似和上近似，但最优的和结构的(即具有所需的特殊性质)近似的开发要差得多。 我们计划开发一系列抽象度量，可用于各种类别的集合、关系结构和属性。此外，我们希望通过一系列保持所需属性(在标准关系理论和粗糙集设置中)的上下近似来模拟度量的概念。在这两种情况下，找到一些有效的算法和支持软件是一个长期的最终目标。

The project deals with two subjects, first involves concurrency', the second approximate reasoning'. Concurrent systems 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. Our general aim is to develop a framework, based on the concept of generalized causality' modelled by discrete relational structures' and generalized traces' (both proposed by Janicki and Koutny), to support the design and the verification of sophisticated concurrent systems. When empirical data are represented as some formal structures, the outcome may not have all required properties. For example any ranking relations should at least be a partial order, but a relation obtained by various subjective judgments may include cycles. The problem is how to find the best approximation' of a given structure by a structure with specific properties. While rough sets' handle lower and upper approximations exceptionally well, optimal' and structural' (i.e. having desired special properties) approximations are much less developed. We plan to develop a family of abstract metrics that can be used for various classes of sets, relational structures and properties. Moreover, we want to simulate the concept of a metric by a sequence of lower' and upper' approximations that preserve the desired properties (in both the standard theory of relations and rough sets settings). In both cases finding some efficient algorithms and supporting software is a long term ultimate goal.