Towards a Theory of Pragmatic Information

[2403.12324] Towards a Theory of Pragmatic Information Skip to main content Search Submit Donate Log in Computer Science > Information Theory arXiv:2403.12324 (cs) [Submitted on 18 Mar 2024 ( v1 ), last revised 27 Aug 2026 (this version, v8)] Title: Towards a Theory of Pragmatic Information Authors: Edward D. Weinberger View PDF HTML (experimental) Abstract: Standard information theory says nothing about how much meaning is conveyed by a message. We fill this gap with a quantitative definition of ``pragmatic information'', the amount of meaning in a message relevant to a particular decision, a definition that is close to, but not identical with previous definitions. Here, we posit that such a message updates a random variable, $\omega$, that informs the decision. The pragmatic information of a single message is then defined as the Kulback-Leibler divergence between the prior and posterior probabilities of $\omega$; the pragmatic information of a message ensemble is the expected value of the pragmatic information of the ensemble's component messages. Canonical standard information theory results justify these definitions, most notably that that the pragmatic information of a single message is the expected difference between the shortest binary encoding of $\omega$ under the {\it a priori} and {\it a posteriori} distributions. We also show that the average of the pragmatic values of individual messages, when sampled a large number of times from the ensemble, approaches its expected value.\\ Pragmatic information is non-negative and additive for independent decisions and ``pragmatically independent'' messages. Also, pragmatic information is the information analogue of free energy: just as free energy quantifies the part of a system's total energy available to do useful work, so pragmatic information quantifies the information actually used in making a decision.\\ We sketch 3 applications: the single play of a slot machine, a.k.a. a ``one armed bandit'', with an unknown payout probability; a characterization of the rate of biological evolution in the so-called ``quasi-species'' model; and a reformulation of the efficient market hypothesis of finance. We note the importance of the computational capacity of the receiver in each case. Comments: 18 pages, 1 figure Subjects: Information Theory (cs.IT) ACM classes: H.1.1 Cite as: arXiv:2403.12324 [cs.IT] (or arXiv:2403.12324v8 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2403.12324 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Edward D. Weinberger [ view email ] [v1] Mon, 18 Mar 2024 23:33:58 UTC (13 KB) [v2] Mon, 22 Apr 2024 03:00:06 UTC (15 KB) [v3] Sun, 4 Aug 2024 21:58:28 UTC (16 KB) [v4] Sat, 5 Oct 2024 04:58:05 UTC (16 KB) [v5] Wed, 20 Nov 2024 20:10:06 UTC (16 KB) [v6] Thu, 6 Feb 2025 21:49:56 UTC (55 KB) [v7] Tue, 18 Aug 2026 04:09:22 UTC (55 KB) [v8] Thu, 27 Aug 2026 05:45:21 UTC (56 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cs.IT < prev | next > new | recent | 2024-03 Change to browse by: cs math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Knowledge, Pragmatics, and Error#744965
• Pragmatic Information, Computation, and the Efficient Market Hypothesis#793041
• Pragmatic Information, Computation, and the Efficient Market Hypothesis#789037
• Understanding pragmatics#465866
• Pragmatism : A learning theory for the future#86443