{
  "annotation_id": "86895981-4249-42a8-81bb-ab99ce3b921b",
  "date_created": "2026-03-02T18:01:56.502000Z",
  "date_modified": "2026-03-02T18:01:56.502000Z",
  "file_hash": "4fa5800cdbc7380ff305b8c2211e7f572d1602c81bc7a522becbbb8174c57334",
  "private": false,
  "record": {
    "abstract": "We produce a probabilistic space from logic, both classical and quantum,\nwhich is in addition partially ordered in such a way that entropy is monotone.\nIn 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\non {1,...,n}) can be fully and faithfully represented by the pair consisting of\nthe abstraction D^n (=the object up to isomorphism) of a partially ordered set\n(\\Delta^n,\\sqsubseteq), and, Shannon entropy; 2. D^n itself can be obtained via\na systematic purely order-theoretic procedure (which embodies introduction of\npartiality of knowledge) on an (algebraic) logic. This procedure applies to any\nposet A; D_A\\cong(\\Delta^n,\\sqsubseteq) when A is the n-element powerset and\nD_A\\cong(\\Omega^n,\\sqsubseteq), the domain of mixed quantum states, when A is\nthe lattice of subspaces of a Hilbert space.\n  (We refer to http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-02-07.html\nfor a domain-theoretic context providing the notions of approximation and\ncontent.)",
    "arxiv_id": "quant-ph/0212065",
    "authors": [
      "Bob Coecke"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "math-ph",
      "math.LO",
      "math.MP",
      "math.PR"
    ],
    "journal_ref": "ENTCS - MFPS 2003",
    "title": "Entropic Geometry from Logic",
    "url": "https://arxiv.org/abs/quant-ph/0212065"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "da57ef3e-3945-426a-8d04-65aea3696987",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}