Negation as failure  

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Kunstformen der Natur (1904) by Ernst Haeckel
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Kunstformen der Natur (1904) by Ernst Haeckel

Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive <math>\mathrm{not}~p</math> (i.e. that <math>~p</math> is assumed not to hold) from failure to derive <math>~p</math>. Note that <math>\mathrm{not} ~p</math> can be different from the statement <math>\neg p</math> of the logical negation of <math>~p</math>, depending on the completeness of the inference algorithm and thus also on the formal logic system.

Negation as failure has been an important feature of logic programming since the earliest days of both Planner and Prolog. In Prolog, it is usually implemented using Prolog's extralogical constructs.




Unless indicated otherwise, the text in this article is either based on Wikipedia article "Negation as failure" or another language Wikipedia page thereof used under the terms of the GNU Free Documentation License; or on original research by Jahsonic and friends. See Art and Popular Culture's copyright notice.

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