In this paper, we present CogNet, a knowledge base (KB) dedicated to integrating three types of knowledge: (1) linguistic knowledge from FrameNet, which schematically describes situations, objects and events. (2) world knowledge from YAGO, Freebase, DBpedia and Wikidata, which provides explicit knowledge about specific instances. (3) commonsense knowledge from ConceptNet, which describes implicit general facts. To model these different types of knowledge consistently, we introduce a three-level unified frame-styled representation architecture. To integrate free-form commonsense knowledge with other structured knowledge, we propose a strategy that combines automated labeling and crowdsourced annotation. At present, CogNet integrates 1,000+ semantic frames from linguistic KBs, 20,000,000+ frame instances from world KBs, as well as 90,000+ commonsense assertions from commonsense KBs. All these data can be easily queried and explored on our online platform, and free to download in RDF format for utilization under a CC-BY-SA 4.0 license. The demo and data are available at http://cognet.top/.