Negation as failure in Prolog is a procedural behavior?

Question

I have a little question about the negation as failure in Prolog language:

This is a question more theoretical than practical because I have clear h

Answer 1

Programs that make use of cut (!) are most of the time sensitive to the ordering of goals and clauses in their meaning and not only in their termination, so they are often not declarative.

The negation as failure (\+) ecapsulates in a certain way the cut. It is defined and even implemented by most Prolog systems as follows:

\+ X :- X, !, fail.
\+ _ .

Although it hints a logical meaning and thus declarativity, the negation as failure is still sensitive to ordering of goals. Here is an example. Assume we have the following database:

p(a).
q(b,c).

Then the following query produces X=a as a solution:

?- p(X), \+ q(X,Y).
X = a.

But if the arguments of the conjunction (,)/2 switch side, a different result is obtained:

?- \+ q(X,Y), p(X).
false.

Ergo, negation as failure is not declarative per se. For ground term flow of arguments, negation as failure sneeks in an existential quantifiers. So a query of the form:

 ?- A(X), \+ B(X,Y).

Has essentially the meaning that it quantifies the fresh variables Y inside the negation:

 ?- A(X), ~ exists Y B(X,Y).

So in the above example where conjunction is switched, the set of fresh variables in the negation as failure changes, thats why different solutions are obtained.

Bye

Answer 2

I disagree with 'limitations of the logic'.

The same would be

likes(mary,X) :- not(snake(X)) , animal(X).

Because Prolog uses a depth-first-search some things can be expressed in an shorter way that then depends on the depth-first-search backtracking algorithm.

x :- a, !, b.
x :- c.
x :- d.

is the same as

x :- a, b.
x :- not(a), c.
x :- not(a), d.