{
  "id": "1805.09437",
  "version": "v1",
  "published": "2018-05-23T21:39:30.000Z",
  "updated": "2018-05-23T21:39:30.000Z",
  "title": "Relational Hypersequents for Modal Logics",
  "authors": [
    "Samara Burns",
    "Richard Zach"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We investigate a new approach to modal hypersequents, called relational hypersequents, which incorporates an accessibility relation along the hypersequent. These systems are an adaptation of Restall's 2009 cut-free complete hypersequent system for S5. Variation between modal systems in the relational framework occurs only in the presence or absence of structural rules, which conforms to Do\\v{s}en's principle. All systems are modular except for that of S5. We provide the first cut-free completeness result for K, T, and D, and show how this method fails in the case of B and S4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T21:39:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B45",
      "03F05"
    ],
    "keywords": [
      "relational hypersequents",
      "modal logics",
      "first cut-free completeness result",
      "cut-free complete hypersequent system",
      "relational framework occurs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}