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Reference: Bob Coecke, (2003). Entropic geometry from logic. Electronic Notes in Theoretical Computer Science, 83, 39–53.Citable link to this page:

 

Entropic geometry from logic

Abstract: We establish the following equation:Quantitative Probability = Logic + Partiality of Knowledge + EntropyI.e.: 1. A finitary probability space Δn (= all probability measures on {1,…, n}) can be fully and faithfully represented by the pair consisting of the abstraction Dn (= the object up to isomorphism) of the partially ordered set (Δn , ⊑) introduced in [3], and, Shannon entropy; 2. Dn itself can be obtained via a systematic purely order-theoretic procedure (which embodies introduction of partiality of knowledge) on an (algebraic) logic. This procedure applies to any poset A; DA ≅ (Δn ,⊑) when A is the n-element powerset and DA ≅ (Ωn, ⊑), the domain of mixed quantum states also introduced in [3], when A is the lattice of subspaces of a Hilbert space.

Publication status:PublishedPeer Review status:Peer reviewedVersion:Publisher's versionNotes:Copyright © 2003 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/

Bibliographic Details

Publisher: Elsevier

Publisher Website: http://www.elsevier.com/

Host: Electronic Notes in Theoretical Computer Sciencesee more from them

Publication Website: http://www.journals.elsevier.com/electronic-notes-in-theoretical-computer-science

Issue Date: 2003

Copyright Date: 2003

pages:39–53Identifiers

Doi: https://doi.org/10.1016/S1571-0661(03)50003-2

Issn: 1571-0661

Urn: uuid:f9e800e9-7a7c-42f3-8fca-113b85ad5a0a Item Description

Type: Article: post-print;

Language: en

Version: Publisher's versionSubjects: Mathematics Tiny URL: ora:9774

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Author: Bob Coecke - institutionUniversity of Oxford facultyMathematical, Physical and Life Sciences Division - Department of Computer Sc

Source: https://ora.ox.ac.uk/objects/uuid:f9e800e9-7a7c-42f3-8fca-113b85ad5a0a



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