Editing Prolog (section)

=== Negation ===
The built-in Prolog predicate <code>\+/1</code> provides [[negation as failure]], which allows for [[non-monotonic logic|non-monotonic]] reasoning. The goal <code>\+ illegal(X)</code> in the rule

<syntaxhighlight lang="prolog">legal(X) :- \+ illegal(X).</syntaxhighlight>

is evaluated as follows: Prolog attempts to prove <code>illegal(X)</code>. If a proof for that goal can be found, the original goal (i.e., <code>\+ illegal(X)</code>) fails. If no proof can be found, the original goal succeeds. Therefore, the <code>\+/1</code> prefix operator is called the "not provable" operator, since the query <code>?- \+ Goal.</code> succeeds if Goal is not provable. This kind of negation is [[Soundness|sound]] if its argument is [[Ground expression|"ground"]] (i.e. contains no variables). Soundness is lost if the argument contains variables and the proof procedure is complete. In particular, the query <code>?- legal(X).</code> now cannot be used to enumerate all things that are legal.