Toward a Formal Multiscale Architectural Framework for Emerging Properties Analysis in Systems of Systems

Systems of systems (SoSs) are composed of multiple operationally and managerially independent systems whose cooperation may lead to the apparition of emergent behaviors. Analysis of constituents and emergent properties is a cornerstone of SoSs. However, systems constituting a SoS may be arbitrarily complex. Therefore, precise modeling of SoSs may produce an enormous amount of information. Analyzing and modeling SoSs is thus a difficult task: how to conciliate complexity and provability of existence/absence of (emergent) properties ? Multiscale architecture modeling is appropriate for handling the inherent complexity of SoSs. Multiscale modeling enables to look at a problem simultaneously from different scales and different levels of detail. It takes advantage of data available at distinct scales, accordingly managing the complexity of behavior involved. Existing works regarding multiscale software architecture often specify a set of fixed views with loose definition of scales and scale dimensions, dramatically restricting scales usage. Furthermore, specification of scale changes have been mildly studied and are often handled as simple refinements. Yet, an adequate representation of model transformations is a key-factor for enabling system analysis. In this paper, we firstly present the formal definition of two scale dimensions: extend and grain. Extend allows to flexibly consider various subsystems, while grain specify different level of details. We formally define scale changes in this context and study their impact on system (emergent) properties.