Decomposing global quantitative properties into local ones

In this paper we address the problem of identifying what local properties the sub-components of a system have to satisfy in order to guarantee a (security) property on the behaviour of the whole system. We associate each action with a value. Hence, we end up with quantitative properties on them, which are specified through a modal logic equipped with a parametric algebraic structure (i.e., a c-semiring). The aim is to have a value related to the satisfaction of a formula. Starting from the behaviour of a general distributed system (or context), we propose a formal approach to decompose a global quantitative property into the local quantitative properties to be satisfied by its sub-contexts.