A rigorous information-theoretic framework that incorporates logical deductive reasoning directly into the communication process. Classical Shannon theory bounds the bits needed to encode symbols while excluding semantics; here, when the receiver can perform sound and (strongly) complete logical inference, any message deducible from what it already knows conveys zero information. Building on Carnap and Bar-Hillel's semantic information theory, rate-distortion theory, and source coding with side information (Slepian-Wolf and Wyner-Ziv), the framework derives sharp upper and lower bounds on communication cost, showing efficiency gains beyond the classical entropy limit across settings with asymmetric knowledge, partial information sharing, and misinformation, illustrated with propositional logic and practical codes.
Presents, for the first time, a Shannon-style information-theoretic analysis of a communication system in which the receiver is equipped with a deductive reasoning (logical inference) capability. Sha…