{
  "id": "2406.03265",
  "version": "v1",
  "published": "2024-06-05T13:41:33.000Z",
  "updated": "2024-06-05T13:41:33.000Z",
  "title": "Unification with Simple Variable Restrictions and Admissibility of $Π_{2}$-rules",
  "authors": [
    "Rodrigo Nicolau Almeida",
    "Silvio Ghilardi"
  ],
  "comment": "22 pages, Accepted at AIML 2024",
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We develop a method to recognize admissibility of $\\Pi_{2}$-rules, relating this problem to a specific instance of the unification problem with linear constants restriction, called here \"unification with simple variable restriction\". It is shown that for logical systems enjoying an appropriate algebraic semantics and a finite approximation of left uniform interpolation, this unification with simple variable restriction can be reduced to standard unification. As a corollary, we obtain the decidability of admissibility of $\\Pi_{2}$-rules for many logical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T13:41:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple variable restriction",
      "admissibility",
      "left uniform interpolation",
      "appropriate algebraic semantics",
      "logical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}