{
  "id": "2210.09630",
  "version": "v1",
  "published": "2022-10-18T06:58:01.000Z",
  "updated": "2022-10-18T06:58:01.000Z",
  "title": "Completeness of Tableau Calculi for Two-Dimensional Hybrid Logics",
  "authors": [
    "Yuki Nishimura"
  ],
  "comment": "27 pages. 5 figures",
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau calculus for Hybrid dependent Product Logic (HdPL), where one dimension depends on the other. In addition, we add the special rule to the tableau calculus for HdPL and show that it is still sound and complete. All of them lack termination, however.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-18T06:58:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B60"
    ],
    "keywords": [
      "two-dimensional hybrid logics",
      "completeness",
      "hybrid dependent product logic",
      "complete tableau calculus",
      "hybrid product logic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}