singleton variables in prolog query - prolog

Question

I am new to Prolog and running into a problem. When I ask the query ?-grandfather(daniel,george) on the data below, I get the wrong answer. I don't understand why my query doesn't work. I also received a warning message stating that [C,D] are singleton variables. This warning no longer occurs. Again, I'm unsure why.
mother(jules,mary).
mother(jules,martha).
mother(jules,andy).
mother(mary,annie).
mother(mary,george).
mother(martha,jesse).
mother(martha,june).
mother(june,camile).
father(daniel,mary).
father(daniel,martha).
father(daniel,andy).
father(adrian,annie).
father(adrian,george).
father(carlo,camile).
brothers(A,B):-father(C,A),father(C,B);mother(D,A),mother(D,B).
grandfather(E,W):-father(E,father(C,W));father(E,mother(D,W)).

Answer 1

You can write your grandfather query more simply:
grandfather(E,W):-father(E,A),father(A,W).
grandfather(E,W):-father(E,A),mother(A,W).
or
grandfather(E,W):-father(E,A),father(A,W);father(E,A),mother(A,W).
and now:
6 ?- grandfather(daniel,george).
true .
7 ?- grandfather(daniel,annie).
true .
Here, we ask Prolog to find the grandson of E where: E is the father of A and A is the father/mother of W.
Or more specifically, to check if daniel has a grandson named george. Prolog checks: daniel has a daughter mary and mary has a son george. So it would return true. If you trace it, you see:
[trace] 3 ?- grandfather(daniel,george).
Call: (6) grandfather(daniel, george) ? creep
Call: (7) father(daniel, _G1931) ? creep
Exit: (7) father(daniel, mary) ? creep
Call: (7) father(mary, george) ? creep
Fail: (7) father(mary, george) ? creep
Redo: (7) father(daniel, _G1931) ? creep
Exit: (7) father(daniel, martha) ? creep
Call: (7) father(martha, george) ? creep
Fail: (7) father(martha, george) ? creep
Redo: (7) father(daniel, _G1931) ? creep
Exit: (7) father(daniel, andy) ? creep
Call: (7) father(andy, george) ? creep
Fail: (7) father(andy, george) ? creep
Redo: (6) grandfather(daniel, george) ? creep
Call: (7) father(daniel, _G1931) ? creep
Exit: (7) father(daniel, mary) ? creep
Call: (7) mother(mary, george) ? creep
Exit: (7) mother(mary, george) ? creep
Exit: (6) grandfather(daniel, george) ? creep
true .
[C,D] are singleton variables indicates that there is one or more variable in the clause that appears only once. This isn't affecting the program, you can still run your queries.
Singleton Variables on SWI Documentation

Answer 2

Thanks for the answer, one last question, i tried to do a rule for cousins like this
cousins(X,Y):-mother(A,X),mother(B,Y),mother(D,A),mother(D,B),father(C,A),father(C,B).
it states that if the mother of X and the mother of Y have the same mother and father X,Y are cousins. but when i ask the query ?- cousins(annie,george) prolog answers YES, and it should not be that way because annie and george are brothers, so i guess there must be a logical mistake
A and B (Mothers of X and Y) can be equal, that is why it gives Yes to brothers.
You should specify that they don't have the same mother and father (A\=B).
Off question:
Using "parent" can reduce your coding in this kind of problems (family trees).
mother(A,B) :- parent(A,B).
Or even:
mother(A,B) :- parent(A,B), female(A).
This way you don't need to apply the cousin problem (or any of this kind, like brothers) to the mother and the father.
In the brothers you have:
brothers(A,B):-father(C,A),father(C,B);mother(D,A),mother(D,B).
It could be:
brothers(A,B):-parent(X,A),parent(X,B).