{
  "id": "2303.09934",
  "version": "v1",
  "published": "2023-03-17T12:50:15.000Z",
  "updated": "2023-03-17T12:50:15.000Z",
  "title": "Decidability of modal logics of non-$k$-colorable graphs",
  "authors": [
    "Ilya Shapirovsky"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We consider the bimodal language, where the first modality is interpreted by a binary relation in the standard way, and the second is interpreted by the relation of inequality. It follows from Hughes (1990), that in this language, non-$k$-colorability of a graph is expressible for every finite $k$. We show that modal logics of classes of non-$k$-colorable graphs (directed or non-directed), and some of their extensions, are decidable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-17T12:50:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B45",
      "F.4.1"
    ],
    "keywords": [
      "modal logics",
      "colorable graphs",
      "decidability",
      "bimodal language",
      "standard way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}