{
  "annotation_id": "799c0eed-634b-4ebc-820c-1ae175cdcea6",
  "date_created": "2026-03-02T18:02:20.540000Z",
  "date_modified": "2026-03-02T18:02:20.540000Z",
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  "record": {
    "abstract": "In this paper we present the fundamentals of the so-called algebraic approach\nto propositional quantum logics. We define the set of formulas describing\nquantum reality as a free algebra freely generated by the set of quantum\npropositional variables. We define the general notion of logic as a structural\nconsequence operation. Next we introduce the concept of logical matrices\nunderstood as a models of quantum logics. We give the definitions of two\nquantum consequence operations defined in these models.",
    "arxiv_id": "quant-ph/0507209",
    "authors": [
      "Piotr Wilczek"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-006-9060-0",
    "journal_ref": "International Journal of Theoretical Physics, 45, No. 4, 695-705\n  (2006)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Model-Theoretic Investigations into Consequence Operation (Cn) in   Quantum Logics. An Algebraic Approach",
    "url": "https://arxiv.org/abs/quant-ph/0507209"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2d0b317c-afc7-4d53-af2a-7e1c175bef7a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}