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  "body": "\n## Summary\n\nA Horn clause is a disjunction of literals in which at most one literal is unnegated.\nSuch a clause can be read as a rule: \"if all of these hold, then that holds\".\nWith no unnegated literal, it is a constraint: \"these do not all hold\".\nSatisfiability of a [[conjunctive normal form|0B3D4C8YF2]] made of Horn clauses can be decided in polynomial time, unlike general [[satisfiability|QN7M1JCGT9]].\nHorn clauses are the basis of logic programming, and their first-order universal forms axiomatize [[universal Horn classes|9A4CYWXPEA]] and [[quasivarieties|WRXEKT4NQS]].\n\n## Explanations\n\n### L1 human\n\nThe clause $\\neg p \\vee \\neg q \\vee r$ says the same as \"if $p$ and $q$, then $r$\".\nRules of this shape can be chained: from known facts one keeps deriving new facts until nothing changes.\nThis is why Horn formulas are easy to solve, while clauses such as $p \\vee q$, which allow a choice, make satisfiability hard in general.\nA clause with no positive literal, such as $\\neg p \\vee \\neg q$, says \"not both $p$ and $q$\".\n",
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