{
  "aliases": [
    "weak-excluded-middle",
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  "body": "\n## Statement\n\nA particularly well-studied intermediate logic is given by De Morgan logic, which adds the axiom $\\neg P \\lor \\neg\\neg P$ to intuitionistic logic, which is sometimes called the law of the weak excluded middle.\n\nThis is equivalent to a few other statements:\n\n- Satisfying all of [[De Morgan's laws|09PKJKA6J0]] including $\\neg(P\\land Q) \\,\\leftrightarrow\\, \\neg P \\lor \\neg Q$\n- $$(P \\to Q) \\lor (\\neg P \\to \\neg Q)$$\n- $$(P \\to (Q \\lor \\neg R)) \\to ((P \\to Q) \\lor (P \\to \\neg R))$$\n",
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    "aliases": [
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        "locator": "Law of excluded middle, section Analogous laws \u003e Law of the weak excluded middle",
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