This paper develops a principled foundation for goal-oriented semantic communication for logical decision-making. Consider a setting where autonomous agents engage in collaborative perception. In such settings, the volume of sensory data and limited bandwidth often make transmission of raw observations infeasible, requiring intelligent selection of task-relevant information. Because these scenarios are safety-critical, the selection and decision processes must also be transparent and verifiable. To address this, we propose an explainable semantic communication framework grounded in a First-Order Logic (FOL) hierarchical representation of the world. We define semantic information, entropy, conditional entropy, and mutual information by assigning an inductive logical probability measure over semantic structures in the language. Based on these definitions, we formulate a goal-oriented semantic communication objective through semantic rate-distortion theory and, equivalently, through the semantic information bottleneck principle. In this framework, task rules are represented as goal-oriented states, defined as a layer over the world states to capture decision-relevant abstractions. The resulting principle selects evidence that is most informative about these states, aiming to transmit only those FOL clauses most critical for decision-making while preserving logical verifiability. We demonstrate the effectiveness of the approach in a deduction-based safe path-following task within an FOL-based urban environment simulator with multiple dynamic agents.

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