Although they are usually designed for top-notch scalability and flexibility, application-agnostic big data pattern analysis frameworks are seldom exploited in process mining. As the size of event logs and the velocity at which events can be generated grow, however, the need for big data-aware process mining solutions emerges. This work targets the extraction of declarative process constraints. Its key novelty lies in employing an application-agnostic pattern analysis framework, called SIESTA, rather than devising an ad-hoc solution tailored to declarative constraint discovery. The key contribution of our work is threefold: (i) we show how we can build on top of SIESTA to extract the full set of Declare constraints in large event logs in a more efficient and scalable manner than the ad-hoc competitors; (ii) we extend our SIESTA-based approach to operate in an incremental manner, which may be required both when the event logs are very large and when they are continuously updated by new batches of events; and (iii) we demonstrate how our SIESTA-based framework can be extended to mine temporal violations of Declare constraints to support variant analysis. The experimental results show that our solution can ingest and process thousands of events per second even using a commodity machine, it can handle datasets of tens of millions of events, and it is much faster than the competitors in repetitive constraint extraction tasks for larger datasets than the ones that can be handled by the competitors.