{
  "aliases": [
    "empty-theory",
    "free-theory",
    "function-letter",
    "function-symbol-logic",
    "function-symbols",
    "functional-predicate",
    "mapping-logic",
    "uninterpreted-function",
    "uninterpreted-term"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn formal systems particularly mathematical logic, a **function symbol** is a non-logical symbol which represents a [[function|0EPAT51DXQ]] or mapping on the domain of discourse, though, formally, does not need to represent anything at all. Function symbols are a basic component in formal languages to form terms. Specifically, if the symbol $F$ is a function symbol, then given any constant symbol $X$ representing an object in the language, $F(X)$ also represents an object in the language. Similarly, if $T$ is some term in the language, $F(T)$ is also a term. As such, the interpretation of a function symbol must be defined over the whole domain of discourse. Function symbols are a primitive notion, and are therefore not defined in terms of other, more basic concepts.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "empty-theory",
      "free-theory",
      "function-letter",
      "function-symbol-logic",
      "function-symbols",
      "functional-predicate",
      "mapping-logic",
      "uninterpreted-function",
      "uninterpreted-term"
    ],
    "inventory": [
      "30Z1Q9TGRC"
    ],
    "kind": "concept",
    "name": "Function symbol",
    "same_as": {
      "wikidata": "Q5508846",
      "wikipedia": "Function symbol"
    },
    "sources": [
      {
        "locator": "Function symbol",
        "mention": "wikipedia://en/174908",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:174908@r1315877491"
      }
    ],
    "tag": "BXBNDHV1HW"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/BXBNDHV1HW/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/BXBNDHV1HW.md",
  "msc": null,
  "name": "Function symbol",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/BXB/BXBNDHV1HW.md",
  "status": null,
  "tag": "BXBNDHV1HW",
  "uri": "m2://BXBNDHV1HW",
  "url": "https://math2.tamnd.com/wiki/function-symbol/",
  "writing": {
    "tag": "BXBNDHV1HW",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}