Although message-based (business) application integration is based on orchestrated message flows, current modeling languages exclusively cover (parts of) the control flow, while under-specifying the data flow. Especially for more data-intensive integration scenarios, this fact adds to the inherent data processing weakness in conventional integration systems. We argue that with a more data-centric integration language and a relational logic based implementation of integration semantics, optimizations from the data management domain(e.g., data partitioning, parallelization) can be combined with common integration processing (e.g., scatter/gather, splitter/gather). With the Logic Integration Language (LiLa) we redefine integration logic tailored for data-intensive processing and propose a novel approach to data-centric integration modeling, from which we derive the control-and data flow and apply them to a conventional integration system.