Relational learning for knowledge base completion has been receiving considerable attention. Intuitively, rule-based strategies are clearly appealing, given their transparency and their ability to capture complex relational dependencies. In practice, however, pure rule-based strategies are currently not competitive with state-of-the-art methods, which is a reflection of the fact that (i) learning high-quality rules is challenging, and (ii) classical entailment is too brittle to cope with the noisy nature of the learned rules and the given knowledge base. In this paper, we introduce STRiKE, a new approach for relational learning in knowledge bases which addresses these concerns. Our contribution is three-fold. First, we introduce a new method for learning stratified rule bases from relational data. Second, to use these rules in a noise-tolerant way, we propose a strategy which extends k-entailment, a recently introduced cautious entailment relation, to stratified rule bases. Finally, we introduce an efficient algorithm for reasoning based on k-entailment.