{
  "id": "2309.05948",
  "version": "v1",
  "published": "2023-09-12T03:53:36.000Z",
  "updated": "2023-09-12T03:53:36.000Z",
  "title": "Semantical cut-elimination for the provability logic of true arithmetic",
  "authors": [
    "Ryo Kashima",
    "Yutaka Kato"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The quasi-normal modal logic GLS is a provability logic formalizing the arithmetical truth. Kushida (2020) gave a sequent calculus for GLS and proved the cut-elimination theorem. This paper introduces semantical characterizations of GLS and gives a semantical proof of the cut-elimination theorem. These characterizations can be generalized to other quasi-normal modal logics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-12T03:53:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "provability logic",
      "true arithmetic",
      "semantical cut-elimination",
      "quasi-normal modal logic gls",
      "cut-elimination theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}