We can use 2 forms of negation in npl. The first is classical negation, and the second negation by failure. In both cases we can only talk about negation of facts; neither predicates nor definitions can be negated.
assertion : NOT fact DOT
NOT : "not"
With classical negation, a negated fact is equivalent to a non-negated fact. You add a negated fact “not P” to the kb in the same way you add a non-negated fact “P”. If you ask (in a query or in the condition of a rule) for a negated fact, you will only succeed if the negated fact is in the kb. The fundamental meaning of classical negation lies in contradiction: you cannot have both a non-negated fact and its negation in the kb. If you try to do so, the system will not accept it and warn you of the contradiction. And if 2 rules produce contradictory facts, the system will break.
Negation by failure relies on a closed world assumption, i.e., on the assumption that all possible knowledge about the universe of discourse is present in the kb. All true facts are present in the kb, and all facts that are not present in the kb are false. So, if we ask a negated fact “not P”, the system need not look for it; it can look for “P”, and if it is not found, our query will succeed.
arith : COUNT fact
COUNT : "count"
So, negation by failure is basically a matter of counting facts. npl allows us to count facts in rules. If you count a fact like count johnny [goes to hollywood] at 3, you will obtain either 1 or 0. So, to set a condition for a negated (by failure) fact, you would add an arithmetic condition like {count johnny [goes to hollywood] at 3 = 0};.
We can also use variables in fact counts. For example, to count how many trips there have been to egipt, we would count Person1 [trips to egipt] at I1.
In npl, counting facts only makes sense if we use its time facilities, and use a further restriction: that we can only make one assertion per instant. Under the assumption of a timeless interpretation, the same set of facts must produce the same set of consecuences under any circumstances, whatever the order they are asserted. If we allow counting sentences in rules, the same set of facts will produce different sets of consecuences depending on the order in which they are added to the kb. However, if we (as we do in npl when we use the present continuous) assume that the past is closed, and the present, in which things change, only accepts one assertion at a time, the order in which we add the facts is part of the general truth, and the same set of facts added in different order would represent different realities.
NOTE: Counting sentences is implemented but not yet exposed in npl, because I’m not sure about the syntax.