{
  "id": "2208.11354",
  "version": "v1",
  "published": "2022-08-24T08:05:27.000Z",
  "updated": "2022-08-24T08:05:27.000Z",
  "title": "Non-distributive positive logic as a fragment of first-order logic over semilattices",
  "authors": [
    "Jim de Groot"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs of states from one model to single states from another. En route to this result we use a more traditional notion of simulations and prove a Hennessy-Milner style theorem for it, using an analogue of modal saturation called meet-compactness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-24T08:05:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-order logic",
      "semilattices",
      "hennessy-milner style theorem",
      "single-sorted first-order language",
      "relate pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}