DISCD: Distributed Lossy Semantic Communication for Logical Deduction of Hypothesis

In this paper, we address hypothesis testing in a distributed network of nodes, where each node has only partial information about the State of the World (SotW) and is tasked with determining which hypothesis, among a given set, is most supported by the data available within the node. However, due to each node's limited perspective of the SotW, individual nodes cannot reliably determine the most supported hypothesis independently. To overcome this limitation, nodes must exchange information via an intermediate server. Our objective is to introduce a novel distributed lossy semantic communication framework designed to minimize each node's uncertainty about the SotW while operating under limited communication budget. In each communication round, nodes determine the most content-informative message to send to the server. The server aggregates incoming messages from all nodes, updates its view of the SotW, and transmits back the most semantically informative message. We demonstrate that transmitting semantically most informative messages enables convergence toward the true distribution over the state space, improving deductive reasoning performance under communication constraints. For experimental evaluation, we construct a dataset designed for logical deduction of hypotheses and compare our approach against random message selection. Results validate the effectiveness of our semantic communication framework, showing significant improvements in nodes' understanding of the SotW for hypothesis testing, with reduced communication overhead.