Modelling Uncertainty in Architectures of Parametric Component-Based Systems

In this paper, we propose a logic-based characterization of uncertainty in architectures of parametric component-based systems, where the parameter is the number of instances of each component type. For this, we firstly introduce an extended propositional interaction logic over De Morgan algebras and we show that its formulas can encode the uncertainty of several architectures applied in systems with a finite number of components. In turn, we introduce a first-order extended interaction logic over De Morgan algebras which is applied for modelling uncertainty in the interactions of well-known parametric architectures. Moreover, we prove that the equivalence problem for a large class of formulas of that logic is decidable in doubly exponential time by providing an effective translation to fuzzy recognizable series. For any such formula over a totally ordered De Morgan algebra, we further prove that we can compute in exponential time the set of sequences of parametric fuzzy interactions which ensure the trustworthiness of the formula according to a particular threshold.