{
  "id": "1408.2125",
  "version": "v2",
  "published": "2014-08-09T15:16:28.000Z",
  "updated": "2015-09-23T07:53:16.000Z",
  "title": "A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments",
  "authors": [
    "Thomas Seiller"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry of interaction which interprets proofs as operators in a von Neumann algebra. The expressivity of the logic soundly interpreted in this model is dependent on properties of a MASA which is a parameter of the interpretation. We also unveil the essential role played by MASAs in previous geometry of interaction constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-09T15:16:28.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-23T07:53:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B70",
      "03F52",
      "03B47",
      "47N99",
      "46L99"
    ],
    "keywords": [
      "maximal abelian sub-algebras",
      "linear logic fragments",
      "correspondence",
      "von neumann algebra",
      "girards hyperfinite geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2125S"
    }
  }
}