Lossy Semantic Communication for the Logical Deduction of the State of the World

TL;DR

This paper proposes a lossy semantic communication method that efficiently transmits logical descriptions of the world to reduce uncertainty and improve deductive task performance within limited bandwidth.

Contribution

It introduces an algorithm that maximizes semantic content transmission by estimating logical probabilities efficiently, enabling effective deduction with minimal data.

Findings

Reduces uncertainty about the world state with fewer bits.

Improves deductive task accuracy compared to baseline methods.

Demonstrates effectiveness on FOLIO and custom datasets.

Abstract

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.