{
  "id": "1407.5812",
  "version": "v1",
  "published": "2014-07-22T10:34:04.000Z",
  "updated": "2014-07-22T10:34:04.000Z",
  "title": "Ł-Axiomatizability in intermediate and normal modal logics",
  "authors": [
    "Alex Citkin"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "A set $F$ of formulas is complete relative to a given class of logics, if every logic from this class can be axiomatized by formulas from $F$. A set of formulas $F$ is {\\L}-complete relative to a given class of logics, if every logic of this class can be {\\L}-axiomatized by formulas from $F$, that is, every of these logics can be defined by an $\\L$-deductive system with axioms and anti-axioms from $F$ and inference rules modus ponens, modus tollens, substitution and reverse substitution. We prove that every complete relative to $\\Ext\\Int$ (or $\\Ext\\KF$) set of formulas is {\\L}-complete. In particular, every logic from $\\Ext\\Int$ (or $\\Ext\\KF$) can be {\\L}-axiomatized by Zakharyaschev's canonical formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T10:34:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal modal logics",
      "inference rules modus ponens",
      "intermediate",
      "complete relative",
      "modus tollens"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5812C"
    }
  }
}