{
  "id": "2003.07408",
  "version": "v1",
  "published": "2020-03-16T18:57:02.000Z",
  "updated": "2020-03-16T18:57:02.000Z",
  "title": "Probabilities with Gaps and Gluts",
  "authors": [
    "Dominik Klein",
    "Ondrej Majer",
    "Soroush Rafiee Rad"
  ],
  "categories": [
    "math.LO",
    "math.PR"
  ],
  "abstract": "Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes' and Jeffrey updating and also suggest mechanisms for aggregating information from different sources.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-16T18:57:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B48",
      "03B53",
      "03B42",
      "60A05"
    ],
    "keywords": [
      "probabilities",
      "first degree entailment",
      "non-classical truth values",
      "four-valued propositional logic",
      "information"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}