{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "61THBNS8WE"
    },
    {
      "field": "uses",
      "target": "6BQ71KQ6QT"
    },
    {
      "field": "defines",
      "target": "G8VGTW9P4F"
    },
    {
      "field": "specializes",
      "target": "WJK0YA4GP2"
    }
  ],
  "body": "\n## Summary\n\nModal logic extends [[propositional logic|09K9MWD2QQ]] with operators $\\square$ and $\\lozenge$, read for example as \"necessarily\" and \"possibly\".\nDifferent readings of $\\square$, such as \"it is known that\", \"it will always be true\" or \"it is provable that\", give different modal logics.\nIts usual semantics uses [[Kripke models|NGHWZ9Y7ZV]], which are sets of possible worlds with an accessibility relation.\n\n## Explanations\n\n### L1 human\n\nOrdinary logic says whether a statement is true.\nModal logic can also say whether it must be true, or could be true.\nThe formula $\\square p$ says \"$p$ is necessary\", and $\\lozenge p$ says \"$p$ is possible\".\nFor example, $\\square p \\to p$ says \"what is necessary is true\", which holds for necessity but fails if $\\square$ means \"it is believed that\".\n",
  "commit": "5fc425f97f1f6b11da5892c2948ef8c5d8805665",
  "front": {
    "kind": "concept",
    "msc": [
      "03B45"
    ],
    "name": "Modal logic",
    "same_as": {
      "wikidata": "Q210841",
      "wikipedia": "Modal logic"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Modal_logic"
      }
    ],
    "tag": "C3RZY20ETK"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/C3RZY20ETK/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/C3RZY20ETK.md",
  "msc": [
    "03B45"
  ],
  "name": "Modal logic",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/C3R/C3RZY20ETK.md",
  "status": null,
  "tag": "C3RZY20ETK",
  "uri": "m2://C3RZY20ETK",
  "url": "https://math2.tamnd.com/wiki/modal-logic/",
  "writing": {
    "tag": "C3RZY20ETK",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}