{
  "id": "2204.13401",
  "version": "v1",
  "published": "2022-04-28T10:39:24.000Z",
  "updated": "2022-04-28T10:39:24.000Z",
  "title": "Positive (Modal) Logic Beyond Distributivity",
  "authors": [
    "Nick Bezhanishvili",
    "Anna Dmitrieva",
    "Jim de Groot",
    "Tommaso Moraschini"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We present a duality for non-necessarily-distributive (modal) lattices and use this to study non-necessarily-distributive positive (modal) logic. Our duality is similar to Priestley duality and as such allows us to use similar tools and techniques to study logic. As a result, we prove Sahlqvist correspondence and canonicity for both the propositional logic as well as a modal extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-28T10:39:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributivity",
      "modal extension",
      "similar tools",
      "study logic",
      "sahlqvist correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}