This paper presents a new method for learning typed entailment graphs from text. We extract predicate-argument structures from multiple-source news corpora, and compute local distributional similarity scores to learn entailments between predicates with typed arguments (e.g., person contracted disease). Previous work has used transitivity constraints to improve local decisions, but these constraints are intractable on large graphs. We instead propose a scalable method that learns globally consistent similarity scores based on new soft constraints that consider both the structures across typed entailment graphs and inside each graph. Learning takes only a few hours to run over 100K predicates and our results show large improvements over local similarity scores on two entailment data sets. We further show improvements over paraphrases and entailments from the Paraphrase Database, and prior state-of-the-art entailment graphs. We show that the entailment graphs improve performance in a downstream task.