Abstract: This paper investigates model compositionâoften referred to as "gluing"âwithin the framework of matching logic. Specifically, we examine the systematic combination of existing signatures, variable valuations, theories, and their corresponding models. Our primary objective is to ensure that this composition preserves satisfaction proofs; that is, any theory validated by the individual constituent models is also validated by the resulting composite model. Our definitions are based on a polyadic, sorted variant of matching logic, which has also been expressed in the Rocq proof assistant. Therefore, we outline our definitions with dependent types for this work to serve as a direct blueprint for the mechanization in the short-term future.