Pragmatic information theory links communication to optimal actions
A Mathematical Theory of Pragmatic Information
Information TheoryArtificial IntelligenceRobotics
Summary
Information isn’t always just about sending messages perfectly; it also matters how that information helps achieve goals. The authors propose a new mathematical framework that focuses on the usefulness of information for making decisions and controlling actions, grouping information into levels based on relevance to tasks. They extend classical information theory to include the cost and value of information when guiding behavior, providing limits on how much useful information a system can use given resource constraints. This helps shift focus from transmitting exact symbols to achieving the best outcome with information.
What this means in practice
- •For networked control engineers: Design control systems that optimize the use of information to achieve goals under resource limits using pragmatic information measures.
- •For autonomous system developers: Build autonomous agents that prioritize information based on how it improves decisions and actions rather than symbol accuracy alone.
A theory result. No direct application yet.
Authors
Kai Niu, Ping Zhang
Abstract
We propose a pragmatic information theory unifying communication, control, and decision-making. Its core is the isoteleia mapping, formalizing equifinality: distinct semantic paths leading to the same optimal action are pragmatically equivalent. This induces a three-tier hierarchy of syntactic, semantic, and pragmatic information, each abstraction discarding task-irrelevant distinctions. We develop pragmatic entropy, up/down mutual information, channel capacity, and rate-distortion, and prove three coding theorems generalizing Shannon's classical results. We introduce pragmatic value (VoI) and cost (CoI) of information as decision-theoretic duals to rate-distortion and capacity, respectively, and formulate a Lagrangian dual framework for cross-layer optimization. The pragmatic efficiency bound $\mathcal{E}_p(λ)=\sup_R[Φ_p(R)-λ\,\mathrm{CoI}_p(R)]$ quantifies the maximum net utility any resource-constrained intelligent system can extract, thereby establishing a fundamental behavioral capacity limit---generalizing Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages yield closed-form Gaussian expressions, while dynamic settings are addressed via a Bellman equation for sequential decision-making. This framework provides a rigorous foundation for task-oriented communication, networked control, autonomous systems, and embodied AI, shifting focus from symbol fidelity to the effectiveness of information in guiding actions, and offers a unified mathematical language for next-generation intelligent systems.