A main advantage of Architecture Description Languages (ADL) is their aptitude to facilitate formal analysis and verification of complex software architectures. Since some researchers try to extend them by new techniques, we show in this paper how the use of tile logic as extension of rewriting logic can enforce the ability of existing ADL formalisms to cope with hierarchy and composition features which are more and more present in such software architectures. In order to cover ADL key and generic concepts, our approach is explained through LfP (Language for rapid Prototyping) as ADL offering the possibility to specify the hierarchical behaviour of software components. Then, our contribution goal is to exploit a suitable logic that allows reasoning naturally about software system behaviour, possibly hierarchical and modular, in terms of its basic components and their interactions.