{"paper":{"title":"Entropic Geometry from Logic","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.LO","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Bob Coecke","submitted_at":"2002-12-10T20:27:42Z","abstract_excerpt":"We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation:\n  Quantitative Probability = Logic + Partiality of Knowledge + Entropy.\n  That is: 1. A finitary probability space \\Delta^n (=all probability measures on {1,...,n}) can be fully and faithfully represented by the pair consisting of the abstraction D^n (=the object up to isomorphism) of a partially ordered set (\\Delta^n,\\sqsubseteq), and, Shannon entropy; 2. D^n itself can be obtained via a sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0212065","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0212065/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}