Analysis of Semantic Communication for Logic-based Hypothesis Deduction

2025-08-29

AI Summary

This paper addresses the hypothesis identification problem in semantic communication under first-order logic (FOL), where the sender—without knowledge of the true state of the world (SotW) and under communication constraints—assists the receiver in selecting the hypothesis most consistent with SotW from a candidate set. We propose a posterior-distribution-approximation framework and design a globally optimal truncated water-filling resource allocation strategy, leveraging symmetry and permutation invariance to ensure theoretical optimality while supporting both single- and multi-round messaging. Our method integrates Stirling’s approximation, KKT condition analysis, Bayesian hypothesis testing, and the maximum a posteriori (MAP) decision rule. Experiments demonstrate that, under budget constraints, our approach significantly reduces misclassification rates and achieves faster convergence than random baselines and existing semantic communication schemes.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This work presents an analysis of semantic communication in the context of First-Order Logic (FOL)-based deduction. Specifically, the receiver holds a set of hypotheses about the State of the World (SotW), while the transmitter has incomplete evidence about the true SotW but lacks access to the ground truth. The transmitter aims to communicate limited information to help the receiver identify the hypothesis most consistent with true SotW. We formulate the objective as approximating the posterior distribution at the transmitter to the receiver. Using Stirling's approximation, this reduces to a constrained, finite-horizon resource allocation problem. Applying the Karush-Kuhn-Tucker conditions yields a truncated water-filling solution. Despite the problem's non-convexity, symmetry and permutation invariance ensure global optimality. Based on this, we design message selection strategies, both for single- and multi-round communication, and model the receiver's inference as an m-ary Bayesian hypothesis testing problem. Under the Maximum A Posteriori (MAP) rule, our communication strategy achieves optimal performance within budget constraints. We further analyze convergence rates and validate the theoretical findings through experiments, demonstrating reduced error over random selection and prior methods.

Problem

• Optimizing semantic communication for logic-based hypothesis deduction
• Transmitting limited information to identify consistent hypotheses
• Achieving optimal performance under communication budget constraints

Innovation

• Semantic communication with First-Order Logic
• Truncated water-filling resource allocation solution
• Optimal message selection under budget constraints