{
  "id": "2312.16035",
  "version": "v1",
  "published": "2023-12-26T12:53:37.000Z",
  "updated": "2023-12-26T12:53:37.000Z",
  "title": "On three-valued presentations of classical logic",
  "authors": [
    "Bruno da Ré",
    "Damian Szmuc",
    "Emmanuel Chemla",
    "Paul Égré"
  ],
  "comment": "Review of Symbolic Logic",
  "doi": "10.1017/S1755020323000114",
  "categories": [
    "math.LO"
  ],
  "abstract": "Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-26T12:53:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B05",
      "03B47",
      "03B50"
    ],
    "keywords": [
      "classical logic",
      "three-valued presentations",
      "middle value acts",
      "monotonic consequence relations",
      "boolean normal schemes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}