In this paper, we address the problem of lossy semantic communication to reduce uncertainty about the State of the World (SotW) for deductive tasks in point to point communication. A key challenge is transmitting the maximum semantic information with minimal overhead suitable for downstream applications. Our solution involves maximizing semantic content information within a constrained bit budget, where SotW is described using First-Order Logic, and content informativeness is measured by the usefulness of the transmitted information in reducing the uncertainty of the SotW perceived by the receiver. Calculating content information requires computing inductive logical probabilities of state descriptions; however, naive approaches are infeasible due to the massive size of the state space. To address this, our algorithm draws inspiration from state-of-the-art model counters and employs tree search-based model counting to reduce the computational burden. These algorithmic model counters, designed to count the number of models that satisfy a Boolean equation, efficiently estimate the number of world states that validate the observed evidence. Empirical validation using the FOLIO and custom deduction datasets demonstrate that our algorithm reduces uncertainty and improves task performance with fewer bits compared to baselines.

翻译：本文研究面向点对点通信中演绎任务的有损语义通信问题，旨在降低关于世界状态的不确定性。核心挑战在于以最小开销传输适用于下游应用的语义信息。我们的解决方案是在受限比特预算内最大化语义内容信息，其中世界状态采用一阶逻辑描述，内容信息量通过传输信息在降低接收端感知世界状态不确定性方面的效用进行度量。计算内容信息需要求解状态描述的归纳逻辑概率，但由于状态空间规模巨大，传统方法难以实现。为此，我们借鉴先进模型计数器的思想，提出基于树搜索的模型计数算法以降低计算负担。这类算法计数器专为统计满足布尔方程模型的数量而设计，能高效估算验证观测证据的世界状态数量。基于FOLIO与定制演绎数据集的实验验证表明，相较于基线方法，本算法能以更少的比特数降低不确定性并提升任务性能。