This paper presents a novel approach to improve the interoperability between four semantic resources that incorporate predicate information. Our proposal defines a set of automatic methods for mapping the semantic knowledge included in WordNet, VerbNet, PropBank and FrameNet. We use advanced graph-based word sense disambiguation algorithms and corpus alignment methods to automatically establish the appropriate mappings among their lexical entries and roles. We study different settings for each method using SemLink as a gold-standard for evaluation. The results show that the new approach provides productive and reliable mappings. In fact, the mappings obtained automatically outnumber the set of original mappings in SemLink. Finally, we also present a new version of the Predicate Matrix, a lexical-semantic resource resulting from the integration of the mappings obtained by our automatic methods and SemLink.