{
  "id": "1006.0992",
  "version": "v1",
  "published": "2010-06-04T20:58:45.000Z",
  "updated": "2010-06-04T20:58:45.000Z",
  "title": "From Lawvere to Brandenburger-Keisler: interactive forms of diagonalization and self-reference",
  "authors": [
    "Samson Abramsky",
    "Jonathan Zvesper"
  ],
  "comment": "To appear in the Proceedings of LOFT 2010",
  "categories": [
    "math.LO",
    "cs.GT"
  ],
  "abstract": "We analyze the Brandenburger-Keisler paradox in epistemic game theory, which is a `two-person version of Russell's paradox'. Our aim is to understand how it relates to standard one-person arguments, and why the `believes-assumes' modality used in the argument arises. We recast it as a fixpoint result, which can be carried out in any regular category, and show how it can be reduced to a relational form of the one-person diagonal argument due to Lawvere. We give a compositional account, which leads to simple multi-agent generalizations. We also outline a general approach to the construction of assumption complete models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-04T20:58:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interactive forms",
      "diagonalization",
      "self-reference",
      "assumption complete models",
      "epistemic game theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.0992A"
    }
  }
}