{
  "id": "2402.11249",
  "version": "v1",
  "published": "2024-02-17T11:10:54.000Z",
  "updated": "2024-02-17T11:10:54.000Z",
  "title": "Non-contingecy in a paraconsistent setting",
  "authors": [
    "Daniil Kozhemiachenko",
    "Liubov Vashentseva"
  ],
  "doi": "10.1093/jigpal/jzac081",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study an extension of First Degree Entailment (FDE) by Dunn and Belnap with a non-contingency operator $\\blacktriangle\\phi$ which is construed as \"$\\phi$ has the same value in all accessible states\" or \"all sources give the same information on the truth value of $\\phi$\". We equip this logic dubbed $\\mathbf{K}^\\blacktriangle_\\mathbf{FDE}$ with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the $\\blacktriangle$ operator modelling search for inconsistencies in the provided information. We construct an analytic cut system for the logic and show its soundness and completeness. We prove that $\\blacktriangle$ is not definable via the necessity modality $\\Box$ of $\\mathbf{K_{FDE}}$. Furthermore, we prove that in contrast to the classical non-contingency logic, reflexive, $\\mathbf{S4}$, and $\\mathbf{S5}$ (among others) frames \\emph{are definable}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-17T11:10:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "paraconsistent setting",
      "non-contingecy",
      "first degree entailment",
      "analytic cut system",
      "classical non-contingency logic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}