In this paper, we present a probability graph-based semantic information compression system for scenarios where the base station (BS) and the user share common background knowledge. We employ probability graphs to represent the shared knowledge between the communicating parties. During the transmission of specific text data, the BS first extracts semantic information from the text, which is represented by a knowledge graph. Subsequently, the BS omits certain relational information based on the shared probability graph to reduce the data size. Upon receiving the compressed semantic data, the user can automatically restore missing information using the shared probability graph and predefined rules. This approach brings additional computational resource consumption while effectively reducing communication resource consumption. Considering the limitations of wireless resources, we address the problem of joint communication and computation resource allocation design, aiming at minimizing the total communication and computation energy consumption of the network while adhering to latency, transmit power, and semantic constraints. Simulation results demonstrate the effectiveness of the proposed system.