Semantic communication is envisioned as a promising technique to break through the Shannon limit. However, the existing semantic communication frameworks do not involve inference and error correction, which limits the achievable performance. In this paper, in order to tackle this issue, a cognitive semantic communication framework is proposed by exploiting knowledge graph. Moreover, a simple, general and interpretable solution for semantic information detection is developed by exploiting triples as semantic symbols. It also allows the receiver to correct errors occurring at the symbolic level. Furthermore, the pre-trained model is fine-tuned to recover semantic information, which overcomes the drawback that a fixed bit length coding is used to encode sentences of different lengths. Simulation results on the public WebNLG corpus show that our proposed system is superior to other benchmark systems in terms of the data compression rate and the reliability of communication.