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.

翻译：本文为面向逻辑决策的目标导向语义通信建立了严谨的理论基础。考虑自主代理参与协作感知的场景，在此类场景中，传感数据量庞大与带宽有限往往使得原始观测传输不可行，因此需要智能筛选任务相关信息。由于这些场景关乎安全关键性，选择与决策过程还需具备透明性与可验证性。为此，我们提出一种可解释的语义通信框架，该框架基于一阶逻辑（FOL）对世界进行分层表示。通过为语言中的语义结构赋予归纳逻辑概率测度，我们定义了语义信息、熵、条件熵与互信息。基于这些定义，我们通过语义率失真理论（及其等价形式——语义信息瓶颈原理）构建了目标导向的语义通信目标。在此框架中，任务规则被表示为目标导向状态，定义为覆盖世界状态的抽象层以捕获决策相关抽象信息。所得原理选取对状态最具信息量的证据，旨在仅传输对决策最关键的一阶逻辑子句，同时保持逻辑可验证性。我们在基于一阶逻辑的城市环境仿真器（含多个动态代理）中，通过基于推演的安全路径跟踪任务验证了该方法的有效性。