Commonsense reasoning has long been one of the core problems in NLP, with the rapid progress of commonsense knowledge bases (CSKB), such as ASER, Probase, and ConceptNet. However, previous works ignored linguistic entailments among commonsense knowledge, which measure semantically including/being included a relationship between sentences or assertions. For example, "I drink cola" entails "I drink beverage." Such entailment relations are very intuitive in human cognition but missed in current CSKBs. Linguistic entailments can enrich current CSKB with a hierarchical structure and equip language models intelligence in a cognitive way.