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Semantic communication is a novel communication paradigm which draws inspiration from human communication focusing on the delivery of the meaning of a message to the intended users. It has attracted significant interest recently due to its potential to improve efficiency and reliability of communication, enhance users' quality-of-experience (QoE), and achieve smoother cross-protocol/domain communication. Most existing works in semantic communication focus on identifying and transmitting explicit semantic meaning, e.g., labels of objects, that can be directly identified from the source signal. This paper investigates implicit semantic communication in which the hidden information, e.g., implicit causality and reasoning mechanisms of users, that cannot be directly observed from the source signal needs to be transported and delivered to the intended users. We propose a novel implicit semantic communication (iSC) architecture for representing, communicating, and interpreting the implicit semantic meaning. In particular, we first propose a graph-inspired structure to represent implicit meaning of message based on three key components: entity, relation, and reasoning mechanism. We then propose a generative adversarial imitation learning-based reasoning mechanism learning (GAML) solution for the destination user to learn and imitate the reasoning process of the source user. We prove that, by applying GAML, the destination user can accurately imitate the reasoning process of the users to generate reasoning paths that follow the same probability distribution as the expert paths. Numerical results suggest that our proposed architecture can achieve accurate implicit meaning interpretation at the destination user.