Decentralized storage of data is gaining increased attention as a means to preserve privacy and ownership over personal data. Simultaneously, the share of streaming data on the Web and other applications, e.g. Internet of Things, continues to grow. The large, uncoordinated amount of data streams within these applications requires methods that can coordinate them, especially when a central authority is lacking. We aim to perform said coordination via stream reasoning, using rules and facts to combine and derive information. Decentralized networks, however, present new problems for stream reasoning not yet (fully) addressed in the literature. This includes added expressivity for network heterogeneity, cross-storage referencing and schema variation, out-of-order arrival of data and variance in the representation of time. We aim to propose theoretical solutions that address challenges on temporal expressivity within the network, on out-of-order processing and on the alignment of temporal ontologies. Ultimately, this research aims to provide a solid formal basis for the processing of unbounded streaming data across different data vaults.