{
  "id": "math/0612542",
  "version": "v1",
  "published": "2006-12-19T10:19:50.000Z",
  "updated": "2006-12-19T10:19:50.000Z",
  "title": "Completeness results for many-valued \\Lukasiewicz modal systems and relational semantics",
  "authors": [
    "Georges Hansoul",
    "Bruno Teheux"
  ],
  "comment": "12 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The paper is dedicated to the problem of adding a modality to the \\Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding Kripke models and modal many-valued algebras. Completeness results are considered through the construction of a canonical model. Completeness is obtained for modal finitely-valued logics but also for a modal many-valued system with an infinitary deduction rule. We introduce two classes of frames for the finitely-valued logics and show that they define two distinct classes of Kripke-complete logics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-19T10:19:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B45",
      "03B50"
    ],
    "keywords": [
      "modal systems",
      "relational semantics",
      "infinitary deduction rule",
      "finitely-valued logics",
      "obtaining completeness results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12542H"
    }
  }
}