{
  "annotation_id": "85c05a50-44c6-4254-96c2-5b5374a113e9",
  "date_created": "2026-03-02T18:02:34.481000Z",
  "date_modified": "2026-03-02T18:02:34.481000Z",
  "file_hash": "89ce2d15365d4bb4dac45a2383d8ea46558204a3435f28e618fba12de847c08c",
  "private": false,
  "record": {
    "abstract": "The word \\textit{proposition} is used in physics with different meanings,\nwhich must be distinguished to avoid interpretational problems. We construct\ntwo languages $\\mathcal{L}^{\\ast}(x)$ and $\\mathcal{L}(x)$ with classical\nset-theoretical semantics which allow us to illustrate those meanings and to\nshow that the non-Boolean lattice of propositions of quantum logic (QL) can be\nobtained by selecting a subset of \\textit{p-testable} propositions within the\nBoolean lattice of all propositions associated with sentences of\n$\\mathcal{L}(x)$. Yet, the aforesaid semantics is incompatible with the\nstandard interpretation of quantum mechanics (QM) because of known no-go\ntheorems. But if one accepts our criticism of these theorems and the ensuing SR\n(semantic realism) interpretation of QM, the incompatibility disappears, and\nthe classical and quantum notions of truth can coexist, since they refer to\ndifferent metalinguistic concepts (\\textit{truth} and \\textit{verifiability\naccording to QM}, respectively). Moreover one can construct a quantum language\n$\\mathcal{L}_{TQ}(x)$ whose Lindenbaum-Tarski algebra is isomorphic to QL, the\nsentences of which state (testable) properties of individual samples of\nphysical systems, while standard QL does not bear this interpretation.",
    "arxiv_id": "quant-ph/0611227",
    "authors": [
      "Claudio Garola"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-007-9372-8",
    "journal_ref": "International Journal of Theoretical Physics (2008), 47: 90-103",
    "title": "Physical propositions and quantum languages",
    "url": "https://arxiv.org/abs/quant-ph/0611227"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a808a4a8-d552-478e-9d66-c3ef7dcbd887",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}