{
  "id": "1301.0958",
  "version": "v1",
  "published": "2013-01-06T01:04:50.000Z",
  "updated": "2013-01-06T01:04:50.000Z",
  "title": "Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation",
  "authors": [
    "Angelo Gilio",
    "Giuseppe Sanfilippo"
  ],
  "journal": "International Journal of Approximate Reasoning, vol. 54, no. 4, pp. 513-525, 2013, http://dx.doi.org/10.1016/j.ijar.2012.11.001",
  "doi": "10.1016/j.ijar.2012.11.001",
  "categories": [
    "math.PR",
    "cs.AI",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman-Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F. We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair (F,E|H) the (possibly empty) class K of the subsets S of F such that C(S) implies E|H. We show that the class K satisfies many properties; in particular K is additive and has a greatest element which can be determined by applying a suitable algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-06T01:04:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasi conjunction",
      "probabilistic entailment",
      "conditional event",
      "nonempty subset",
      "p-entailment"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0958G"
    }
  }
}