{
  "id": "2310.11719",
  "version": "v1",
  "published": "2023-10-18T05:38:39.000Z",
  "updated": "2023-10-18T05:38:39.000Z",
  "title": "Representable distributive quasi relation algebras",
  "authors": [
    "Andrew Craig",
    "Claudette Robinson"
  ],
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jonsson and Tarski (1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-18T05:38:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06F05",
      "03B47",
      "03G10"
    ],
    "keywords": [
      "representable distributive quasi relation algebras",
      "definition",
      "representable dqras",
      "representable relation algebras",
      "leave open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}