We present an event structure classification empirically derived from inferential properties annotated on sentence- and document-level Universal Decompositional Semantics (UDS) graphs. We induce this classification jointly with semantic role, entity, and event-event relation classifications using a document-level generative model structured by these graphs. To support this induction, we augment existing annotations found in the UDS1.0 dataset, which covers the entirety of the English Web Treebank, with an array of inferential properties capturing fine-grained aspects of the temporal and aspectual structure of events. The resulting dataset (available at decomp.io) is the largest annotation of event structure and (partial) event coreference to date.