Concurrency and Approximate Reasoning

该项目涉及两个主题，第一个涉及“并行”，第二个“近似推理”。并发系统在人类经验中比比皆是，但它们的充分概念化还没有得到我们的理解。在人类事务和活动的管理和控制中，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、更正式的概念以保持对我们所创建的系统的可靠控制的紧迫性。正确规范的设计和验证其行为的问题的解决方案变得至关重要，和一个令人满意的概念装置，严格的规范和验证变得至关重要。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。我们的总体目标是开发一个框架，基于“广义因果关系”的概念建模的“离散关系结构”和“广义痕迹”（均由Janicki和Koutny提出），以支持复杂的并发系统的设计和验证。 当经验数据表示为某种形式结构时，结果可能不具有所有必需的属性。例如，任何排序关系至少应该是偏序关系，但通过各种主观判断得到的关系可能包含循环。问题是如何用具有特定性质的结构找到给定结构的“最佳近似”。虽然“粗糙集”处理上下近似非常好，但“最佳”和“结构”（即具有所需的特殊性质）近似的发展要少得多。 我们计划开发一个抽象的指标，可用于各种类别的集，关系结构和属性的家庭。此外，我们要模拟度量的概念，通过一系列的“下”和“上”近似，保持所需的属性（在标准理论的关系和粗糙集设置）。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.