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  "body": "\n## Summary\n\nAn MV-algebra is an algebraic structure with a truncated addition $\\oplus$, a negation $\\neg$ and a constant $0$.\nIt is modelled on the unit interval $[0, 1]$ with $x \\oplus y = \\min(1, x + y)$ and $\\neg x = 1 - x$.\nChen Chung Chang introduced MV-algebras in 1958 to give an algebraic proof of the completeness of Łukasiewicz infinite-valued logic, a [[many-valued logic|DWYCKAKXZD]].\nEvery [[Boolean algebra|0XADJKM699]] is an MV-algebra, and MV-algebras play for Łukasiewicz logic the role that Boolean algebras play for classical logic.\nDaniele Mundici showed that MV-algebras correspond to lattice-ordered abelian groups with a strong unit.\n\n## Explanations\n\n### L1 human\n\nIn Łukasiewicz logic a statement can be partly true, with a truth value anywhere between $0$ (false) and $1$ (true).\n\"Not $x$\" has truth value $1 - x$, and a kind of \"or\" adds the truth values but stops at $1$.\nFor example, $0.3 \\oplus 0.5 = 0.8$, while $0.7 \\oplus 0.5 = 1$.\nAn MV-algebra is any structure that obeys the same equations as these operations on $[0, 1]$.\n",
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