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  "body": "\n## Definition\n\nA *literal* is an atomic formula or the negation of an atomic formula; it is *positive* in the first case and *negative* in the second.\nA *clause* is a finite disjunction $L_1 \\vee \\cdots \\vee L_k$ of literals, as in a [[conjunctive normal form|0B3D4C8YF2]].\nA *Horn clause* is a clause in which at most one literal is positive.\n\n## Remarks\n\nA Horn clause with exactly one positive literal is a *definite clause*; one with no positive literal is a *goal clause*.\nA definite clause $\\neg p_1 \\vee \\cdots \\vee \\neg p_n \\vee q$ is equivalent to the implication $p_1 \\wedge \\cdots \\wedge p_n \\rightarrow q$; for $n = 0$ it is the fact $q$.\n\nExample: $\\neg p \\vee \\neg q \\vee r$ is a Horn clause, since only $r$ is positive.\n\nNon-example: $p \\vee q$ is not a Horn clause, since it has two positive literals.\nNo conjunction of Horn clauses is equivalent to it.\nThe satisfying assignments of a conjunction of Horn clauses are closed under the coordinatewise \"and\".\nBut $(1, 0)$ and $(0, 1)$ satisfy $p \\vee q$, while $(0, 0)$ does not.\n\nIn first-order logic, the atoms may be any atomic formulas, and the clause is read as universally quantified over its variables.\n",
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