What happens when information theory accounts for reasoning?

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Shannon's 1948 information theory separated meaning from transmission efficiency — a useful abstraction that powered modern communications but deliberately ignored what recipients could logically deduce from received information. A new paper published in the Proceedings of the National Academy of Sciences extends that foundational framework to explicitly account for reasoning.\n\nThe work, by IBM Research scientists Luis Lastras, Jonathan Lenchner, Barry Trager, Mark Squillante, Chai Wah Wu, and Ronald Fagin, along with collaborators Wojciech Szpankowski (Purdue) and Alexander Gray (Georgia Tech), introduces a sender-receiver model where the receiver has a reasoning capability. The central insight: if a receiver can perform logical deduction, a sender does not need to transmit every fact individually — communication becomes more efficient when senders can transmit information from which receivers can infer additional knowledge.\n\nThe Feynman framing opens the paper: one sentence about atoms enables reconstruction of vast scientific knowledge. Applied to AI, the framework could inform principled approaches to context compression (why send a full knowledge base when a smaller inferential basis suffices?), training data efficiency, and agent-to-agent communication protocols.\n\nThe IBM blog presents theoretical foundations rather than engineering benchmarks. Near-term practical applications for AI systems remain speculative, but PNAS publication in a peer-reviewed venue lends the mathematical framework serious credibility.