{
  "annotation_id": "60c9bb30-932b-4929-8ad7-111bcbf06085",
  "date_created": "2026-03-02T18:02:02.804000Z",
  "date_modified": "2026-03-02T18:02:02.804000Z",
  "file_hash": "71150424bfce1c83ac098c49055e1073f4cc4bc8f48cbc617fb4abd027928db6",
  "private": false,
  "record": {
    "abstract": "It is shown that operations of equivalence cannot serve for building algebras\nwhich would induce orthomodular lattices as the operations of implication can.\nSeveral properties of equivalence operations have been investigated.\nDistributivity of equivalence terms and several other 3 variable expressions\ninvolving equivalence terms have been proved to hold in any orthomodular\nlattice. Symmetric differences have been shown to reduce to complements of\nequivalence terms. Some congruence relations related to equivalence operations\nand symmetric differences have been considered.",
    "arxiv_id": "quant-ph/0310063",
    "authors": [
      "Norman D. Megill",
      "Mladen Pavicic"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1023/B:IJTP.0000006006.18494.1c",
    "journal_ref": "International Journal of Theoretical Physics, Vol. 42, No. 12,\n  2797-2805 (2003).",
    "title": "Equivalences, Identities, Symmetric Differences, and Congruences in   Orthomodular Lattices",
    "url": "https://arxiv.org/abs/quant-ph/0310063"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b043364e-26bb-48d8-8e71-f21ee52f7a3f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}