🤖 AI Summary
Classical Shannon information theory assumes semantic irrelevance, failing to account for logical knowledge held by communicating agents. This work addresses the problem of minimizing communication cost when a sender (Alice) and receiver (Bob) possess partial, possibly heterogeneous, logical knowledge, such that Bob must logically deduce Alice’s private proposition via first-order deduction.
Method: We propose the first semantic-aware communication theory integrating logic-based reasoning with information theory. Crucially, we formally incorporate Bob’s first-order deductive capability into the communication model, establishing a semantics-sensitive transmission paradigm. Combining coding theory, game-theoretic analysis, and algorithm design, we derive tight upper and lower bounds on semantic communication complexity.
Contribution/Results: We introduce the first knowledge-driven communication framework supporting logical inference; derive optimal code-length bounds for multiple semantic scenarios; design an asymptotically optimal algorithm; and empirically demonstrate significant gains in transmission efficiency over classical schemes.
📝 Abstract
Today, the vast majority of the world's digital information is represented using the fundamental assumption, introduced by Claude Shannon in 1948, that ``...the semantic aspects of communication are irrelevant to the engineering problem (of the design of communication systems)...''. Consider, nonetheless, the observation that we often combine a message with other information in order to deduce new facts, thereby expanding the value of such a message. It is noteworthy that to-date, no rigorous theory of communication has been put forth which postulates the existence of deductive capabilities on the receiver's side. The purpose of this paper is to present such a theory. We formally model such deductive capabilities using logic reasoning, and present a rigorous theory which covers the following generic scenario: Alice and Bob each have knowledge of some logic sentence, and they wish to communicate as efficiently as possible with the shared goal that, following their communication, Bob should be able to deduce a particular logic sentence that Alice knows to be true, but that Bob currently cannot prove. Many variants of this general setup are considered in this article; in all cases we are able to provide sharp upper and lower bounds. Our contribution includes the identification of the most fundamental requirements that we place on a logic and associated logical language for all of our results to apply. Practical algorithms that are in some cases asymptotically optimal are provided, and we illustrate the potential practical value of the design of communication systems that incorporate the assumption of deductive capabilities at the receiver using experimental results that suggest significant possible gains compared to classical systems.