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  "body": "\n## Summary\n\nA De Morgan algebra is a bounded [[distributive lattice|0HM0HQCK6N]] with a negation $\\sim$ that is an involution and satisfies [[De Morgan's laws|09PKJKA6J0]].\nUnlike the complement of a [[Boolean algebra|0XADJKM699]], this negation need not satisfy $a \\wedge {\\sim} a = 0$ or $a \\vee {\\sim} a = 1$.\nDe Morgan algebras give the algebraic semantics of several many-valued and relevance logics.\nEvery Boolean algebra is a De Morgan algebra.\n\n## Explanations\n\n### L1 human\n\nTake the numbers from $0$ to $1$ as degrees of truth, with \"and\" as the minimum, \"or\" as the maximum, and \"not $x$\" as $1 - x$.\nThis negation turns \"and\" into \"or\" and back, and doing it twice gives the start again.\nBut the statement \"$x$ and not $x$\" need not be fully false: for $x = 1/2$ it has truth degree $1/2$.\nA De Morgan algebra keeps these rules of negation and drops the laws $x \\wedge {\\sim} x = 0$ and $x \\vee {\\sim} x = 1$.\n",
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