RDF stream reasoning is gaining more and more attention but current research mainly focuses on logical frameworks which aim to formalize the query semantics and enhance the complexity of reasoning ability. These frameworks are evaluated on prototype systems based on a centralized design and suffer from limited scalability. A common way to enhance system scalability is to adopt a distributed approach. Moreover, the study of applying distributed solution for expressive RDF stream reasoning is still missing. In this paper, we explore the ability of modern Big Data platform to handle highly expressive temporal Datalog/Answer Set Programming(ASP) over RDF data streams. In order to achieve our goal, we first discuss some key features to parallelize Datalog/ASP program, and we associate these features to the two well known distributed stream processing models, namely Bulk Synchronous Processing (BSP) and Record-at-A-Time (RAT). We build a technical demonstrator called BigSR on top of Spark(BSP) and Flink(RAT) to support our evaluations, and identify the pros and cons of each model. Our experiments show that, BigSR achieves high throughput beyond million-triples per second using a rather small cluster of machines.