Work in knowledge representation has long struggled to design schemas of entity- and relation-types that capture the desired balance of specificity and generality while also supporting reasoning and information integration from various sources of input evidence. In our "universal schema" approach to knowledge representation we operate on the union of all input schemas (from structured KBs to OpenIE textual patterns) while also supporting integration and generalization by learning vector embeddings whose neighbhorhoods capture semantic implicature. In this talk I will briefly review our past work on a knowledge graph with universal schema relations and entity types, then describe new research in multi-sense embeddings, Gaussian embeddings that capture uncertainty and asymmetries, and logical implicature of new relations through multi-hop relation paths compositionally modeled by recursive neural tensor networks.