{
  "id": "2006.04673",
  "version": "v1",
  "published": "2020-06-08T15:26:28.000Z",
  "updated": "2020-06-08T15:26:28.000Z",
  "title": "Boolean algebras of conditionals, probability and logic",
  "authors": [
    "Tommaso Flaminio",
    "Lluis Godo",
    "Hykel Hosni"
  ],
  "categories": [
    "math.LO",
    "cs.LO",
    "math.PR"
  ],
  "abstract": "This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\\em Boolean algebra of conditionals} from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T15:26:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B48",
      "03G05",
      "68T27",
      "60A05"
    ],
    "keywords": [
      "boolean algebra",
      "conditional events",
      "regard standard two-place conditional probabilities",
      "preferential consequence relations",
      "one-place probability functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}