dorsal/arxiv
View SchemaA Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties
| Authors | Diederik Aerts, Liane Gabora |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402207 |
| URL | https://arxiv.org/abs/quant-ph/0402207 |
| DOI | 10.1108/03684920510575799 |
| Journal | Kybernetes, 34, pp. 167-191, 2005. |
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)
{
"annotation_id": "3fe62f95-fa2b-46f2-afb5-c1a57a861556",
"date_created": "2026-03-02T18:02:07.106000Z",
"date_modified": "2026-03-02T18:02:07.106000Z",
"file_hash": "b1080d3245370084ac854fffe604a471d97cef367f0742931df5725de37439cb",
"private": false,
"record": {
"abstract": "We propose a theory for modeling concepts that uses the\nstate-context-property theory (SCOP), a generalization of the quantum\nformalism, whose basic notions are states, contexts and properties. This theory\nenables us to incorporate context into the mathematical structure used to\ndescribe a concept, and thereby model how context influences the typicality of\na single exemplar and the applicability of a single property of a concept. We\nintroduce the notion `state of a concept\u0027 to account for this contextual\ninfluence, and show that the structure of the set of contexts and of the set of\nproperties of a concept is a complete orthocomplemented lattice. The structural\nstudy in this article is a preparation for a numerical mathematical theory of\nconcepts in the Hilbert space of quantum mechanics that allows the description\nof the combination of concepts (see quant-ph/0402205)",
"arxiv_id": "quant-ph/0402207",
"authors": [
"Diederik Aerts",
"Liane Gabora"
],
"categories": [
"quant-ph"
],
"doi": "10.1108/03684920510575799",
"journal_ref": "Kybernetes, 34, pp. 167-191, 2005.",
"title": "A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties",
"url": "https://arxiv.org/abs/quant-ph/0402207"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b6e453b6-5ec5-4e26-8b5d-a08f4062d3a5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}