{
  "id": "1808.10007",
  "version": "v1",
  "published": "2018-08-29T18:34:00.000Z",
  "updated": "2018-08-29T18:34:00.000Z",
  "title": "Modal Logic With Non-deterministic Semantics: Part I - Propositional Case",
  "authors": [
    "Marcelo E. Coniglio",
    "Luis Fariñas del Cerro",
    "Newton M. Peron"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and extended his hierarchy, proposing weaker six-valued systems in which the T axiom was replaced by the deontic D axiom. Here, we eliminate both axioms, proposing even weaker systems with eight values. Besides, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those systems. We will show that finite deterministic matrices do not characterize any of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T18:34:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B45"
    ],
    "keywords": [
      "modal logic",
      "propositional case",
      "finite deterministic matrices",
      "completeness",
      "axiom holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}