{
  "id": "quant-ph/0402207",
  "version": "v1",
  "published": "2004-02-26T23:24:21.000Z",
  "updated": "2004-02-26T23:24:21.000Z",
  "title": "A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties",
  "authors": [
    "Diederik Aerts",
    "Liane Gabora"
  ],
  "comment": "20 pages, to appear in the journal 'Kybernetes' in the Summer of 2004",
  "journal": "Kybernetes, 34, pp. 167-191, 2005.",
  "doi": "10.1108/03684920510575799",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts (see quant-ph/0402205)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-26T23:24:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combination",
      "single property",
      "quantum mechanics",
      "hilbert space",
      "basic notions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004quant.ph..2207A"
    }
  }
}