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Semantic communications will play a critical role in enabling goal-oriented services over next-generation wireless systems. However, most prior art in this domain is restricted to specific applications (e.g., text or image), and it does not enable goal-oriented communications in which the effectiveness of the transmitted information must be considered along with the semantics so as to execute a certain task. In this paper, a comprehensive semantic communications framework is proposed for enabling goal-oriented task execution. To capture the semantics between a speaker and a listener, a common language is defined using the concept of beliefs to enable the speaker to describe the environment observations to the listener. Then, an optimization problem is posed to choose the minimum set of beliefs that perfectly describes the observation while minimizing the task execution time and transmission cost. A novel top …