Unmanned aerial vehicles (UAVs) are widely used for object detection. However, the existing UAV-based object detection systems are subject to severe challenges, namely, their limited computation, energy and communication resources, which limits the achievable detection performance. To overcome these challenges, a UAV cognitive semantic communication system is proposed by exploiting a knowledge graph. Moreover, we design a multi-scale codec for semantic compression to reduce data transmission volume while guaranteeing detection performance. Considering the complexity and dynamicity of UAV communication scenarios, a signal-to-noise ratio (SNR) adaptive module with robust channel adaptation capability is introduced. Furthermore, an object detection scheme is proposed by exploiting the knowledge graph to overcome channel noise interference and compression distortion. Simulation results conducted on the practical aerial image dataset demonstrate that our proposed semantic communication system outperforms benchmark systems in terms of detection accuracy, communication robustness, and computation efficiency, especially in dealing with low bandwidth compression ratios and low SNR regimes.