{
  "id": "2004.03813",
  "version": "v1",
  "published": "2020-04-08T05:13:07.000Z",
  "updated": "2020-04-08T05:13:07.000Z",
  "title": "Modal completeness of sublogics of the interpretability logic $\\mathbf{IL}$",
  "authors": [
    "Taishi Kurahashi",
    "Yuya Okawa"
  ],
  "comment": "31 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study modal completeness and incompleteness of several sublogics of the interpretability logic $\\mathbf{IL}$. We introduce the sublogic $\\mathbf{IL}^-$, and prove that $\\mathbf{IL}^-$ is sound and complete with respect to Veltman prestructures which are introduced by Visser. Moreover, we prove the modal completeness of twelve logics between $\\mathbf{IL}^-$ and $\\mathbf{IL}$ with respect to Veltman prestructures. On the other hand, we prove that eight natural sublogics of $\\mathbf{IL}$ are modally incomplete. Finally, we prove that these incomplete logics are complete with respect to generalized Veltman prestructures. As a consequence of these investigations, we obtain that the twenty logics studied in this paper are all decidable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-08T05:13:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interpretability logic",
      "study modal completeness",
      "natural sublogics",
      "generalized veltman prestructures",
      "incomplete logics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}