LfP (Language for Prototyping) is an ADL (Architecture Description Language) with a hierarchical and modular structure. In this paper, we propose tile logic (a rewriting logic extension) as a suitable semantic framework for this language. Indeed, it contributes to the formalization of LfP by providing a natural description for concurrency, synchronization and hierarchical composition aspects. A straight consequence of this work is the possibility to describe reconfigurable LfP architectures, and to handle with executable specification in Maude allowing hierarchical formal verification. For further information, please visit this web site.