How neural networks in the human brain represent commonsense knowledge, and complete related reasoning tasks is an important research topic in neuroscience, cognitive science, psychology, and artificial intelligence. Although the traditional artificial neural network using fixed-length vectors to represent symbols has gained good performance in some specific tasks, it is still a black box that lacks interpretability, far from how humans perceive the world. Inspired by the grandmother-cell hypothesis in neuroscience, this work investigates how population encoding and spiking timing-dependent plasticity (STDP) mechanisms can be integrated into the learning of spiking neural networks, and how a population of neurons can represent a symbol via guiding the completion of sequential firing between different neuron populations. The neuron populations of different communities together constitute the entire commonsense knowledge graph, forming a giant graph spiking neural network. Moreover, we introduced the Reward-modulated spiking timing-dependent plasticity (R-STDP) mechanism to simulate the biological reinforcement learning process and completed the related reasoning tasks accordingly, achieving comparable accuracy and faster convergence speed than the graph convolutional artificial neural networks. For the fields of neuroscience and cognitive science, the work in this paper provided the foundation of computational modeling for further exploration of the way the human brain represents commonsense knowledge. For the field of artificial intelligence, this paper indicated the exploration direction for realizing a more robust and interpretable neural network by constructing a commonsense knowledge representation and reasoning spiking neural networks with solid biological plausibility.