{
  "id": "2208.14715",
  "version": "v1",
  "published": "2022-08-31T09:22:18.000Z",
  "updated": "2022-08-31T09:22:18.000Z",
  "title": "Intuitionistic Logic is a Connexive Logic",
  "authors": [
    "Davide Fazio",
    "Antonio Ledda",
    "Francesco Paoli"
  ],
  "comment": "36 pages, submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for CHL; moreover, we suggest a possible computational interpretation of its connexive conditional, and we revisit Kapsner's idea of superconnexivity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T09:22:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "intuitionistic logic",
      "revisit kapsners idea",
      "gentzen-style proof systems",
      "reverse algebraisation paradigm",
      "point regular variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}