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Semantic communication is an emerging paradigm that focuses on understanding and delivering semantics, or meaning of messages. Most existing semantic communication solutions define semantic meaning as the meaning of object labels recognized from a source signal, while ignoring intrinsic information that cannot be directly observed. Moreover, existing solutions often assume the recognizable semantic meanings are limited by a pre-defined label database. In this paper, we propose a novel reasoning-based semantic communication architecture in which the semantic meaning is represented by a graph-based knowledge structure in terms of object-entity, relationships, and reasoning rules. An embedding-based semantic interpretation framework is proposed to convert the high-dimensional graph-based representation of semantic meaning into a low-dimensional representation, which is efficient for channel transmission. We develop a novel inference function-based approach that can automatically infer hidden information such as missing entities and relations that cannot be directly observed from the message. Finally, we introduce a life-long model updating approach in which the receiver can learn from previously received messages and automatically update the reasoning rules of users when new unknown semantic entities and relations have been discovered. Extensive experiments are conducted based on a real-world knowledge database and numerical results show that our proposed solution achieves 76% interpretation accuracy of semantic meaning at the receiver, notably when some entities are missing in the transmitted message.