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Semantic communication (SC) aims to communicate reliably with minimal data transfer while simultaneously providing seamless connectivity to heterogeneous services and users. In this paper, a novel emergent SC (ESC) system framework is proposed and is composed of a signaling game for emergent language design and a neuro-symbolic (NeSy) artificial intelligence (AI) approach for causal reasoning. In order to design the language, the signaling game is solved using an alternating maximization between the communicating node's utilities. The emergent language helps create a context-aware transmit vocabulary (minimal semantic representation) and aids the reasoning process (enabling generalization to unseen scenarios) by splitting complex messages into simpler reasoning tasks for the receiver. The causal description at the transmitter is then modeled (a neural component) as a posterior distribution of the relevant attributes present in the data. Using the reconstructed causal state, the receiver evaluates a set of logical formulas (symbolic part) to execute its task. The nodes NeSy reasoning components are implemented by the recently proposed AI tool called Generative Flow Networks, and they are optimized for higher semantic reliability. The ESC system is designed to enhance the novel metrics of semantic information, reliability, distortion and similarity that are designed using rigorous algebraic properties from category theory thereby generalizing the metrics beyond Shannon's notion of uncertainty. Simulation results validate the ability of ESC to communicate efficiently (with reduced bits) and achieve better semantic reliability than conventional wireless and state-of-the-art systems that do not exploit causal reasoning capabilities.