A mathematical denotation is proposed for the notion of complex software systems whose behavior is specified by rigorous formalisms. Complex systems are described in a recursive way as an interconnection of subsystems by means of architectural connectors. In order to consider the largest family of specification formalisms and architectural connectors, this denotation is essentially formalism, specification and connector independent. For this, we build our denotation on Goguen's institution theory. In this abstract framework, we characterize complexity by the notion of property emergence. This work is a revised and extended version of Aiguier, Le Gall andMabrouki (3rd International Conference on Software Engineering Advanced (ICSEA), IEEE Computer Society Press, 2008).