Concurrency Theory and Non-Numerical Approximation

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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.**