Increasingly huge amounts of data are published on the Web, and generated from sensors and social media. This Big Data challenge poses new scientific and technological challenges and creates new opportunities - thus the increasing attention in academia and industry. Traditionally, logic programming has focused on complex knowledge structures/programs, so the question arises whether and how it can work in the face of Big Data. In this paper, we examine how stratified semantics of logic programming, equivalent to the well-founded semantics for stratified programs, can process huge amounts of data through mass parallelization. In particular, we propose and evaluate a parallel approach using the MapReduce framework. Our experimental results indicate that our approach is scalable and that stratified semantics of logic programming can be applied to billions of facts.