Prolog implying a negative predicate

Have you ever heard about cut in Prolog?

Anyway I don't know much about Prolog standard, but in SWI-Prolog the symbol \+ means negation. I know it don't have to work in every Prolog's interpreter.

You can make the predicate negation with Prolog's cut. The predicate is defined like:

not(Goal) :- call(Goal),!,fail.
not(Goal). 

It means that Goal can't be proven, not the Goal is false. Maybe this Prolog & Cut link will be useful.

The clause "if P then not Q" is logically equivalent to the negative clause "not P OR not Q". As such it is a Horn clause without a positive literal, and as an application of the correspondence of SLD theorem proving and Horn clauses, can be represented in Prolog programming as a goal clause or "query":

?- P, Q.

Let's come back to this idea in a minute.

But the goal clause is perhaps not the sort of representation you have in mind. The facts and rules that constitute a Prolog "knowledgebase" are definite clauses, i.e. Horn clauses each with exactly one positive literal. "If P then not Q" has no positive literal, so in this sense it cannot be represented (as a definite clause).

The goal clause shown above "asks" if P and Q can both be proven. Prolog provides a notion of "negation as failure", so a more natural way to "ask" whether "not P OR not Q" holds would be:

?- not((P,Q)).

Then we would get success if either P or Q fails, and failure if both succeed.

However if your purpose is to assert the negation something in the knowledgebase, Prolog doesn't naturally support this. Depending on your application, there may be a reasonable way to work around the Prolog syntax and accomplish what is needed (there's always an unreasonable way to do it, as you've hinted as with a non_q predicate).