Transitive closure by symmetric relation in prolog

Question

I am a beginner prologue and I want to create a brother relationship.

The relation should be symmetrical, as if the brother (alin, alex) is true, the brother (alex, alin) should also be.

It must also be transitive, as if the brother (alin, alex) and brother (alex, claudiu) were true, brother (alin, claudiu) .

Combining with properties, if the brother (alex, alin) and brother (alex, claudiu) are true, the brother (alin, claudiu) should also be true.

Here is my code:

r_brother(alin, alex).
r_brother(alin, ciprian).
r_brother(alex, claudiu).

s_brother(X, Y) :- r_brother(X, Y).
s_brother(X, Y) :- r_brother(Y, X).

brother(L1, L2) :-
    t_brother(L1, L2, []).

t_brother(L1, L2, _) :-
    s_brother(L1, L2).

t_brother(L1, L2, IntermediateNodes) :-
    s_brother(L1, L3),
    \+ member(L3, IntermediateNodes),
    t_brother(L3, L2, [L3 | IntermediateNodes]).

r_brother - basic ratio

s_brother - ( )

t_brother - , ,

, :

?- brother(X, alin).

:

X = alex ;
X = ciprian ;
X = alin ;
X = alin ;
X = alin ;
X = alin ;
X = alex ;
X = alex ;
X = alex ;
X = alex ;
X = ciprian ;
X = ciprian ;
X = claudiu ;
X = claudiu ;
false.

, , , , .

alin , .

Answer 1

, , , L2 t_brother/3. L1 /2:

brother(L1, L2) :-
  t_brother(L1, L2, [L1]).                   % <-- [L1] instead of []

t_brother(L1, L2, IntermediateNodes) :-
  s_brother(L1, L2),
  \+ member(L2, IntermediateNodes).          % <-- added this check

t_brother(L1, L2, IntermediateNodes) :-      % <-- this clause is unchanged
  s_brother(L1, L3),
  \+ member(L3, IntermediateNodes),
  t_brother(L3, L2, [L3 | IntermediateNodes]).

, :

t_brother(L1, L2, IntermediateNodes) :-
  s_brother(L1, L3),
  \+ member(L3, IntermediateNodes),
  ( L2=L3
  ; t_brother(L3, L2, [L3 | IntermediateNodes])).

Answer 2

( , )

s_brother(X, Y) :- r_brother(X, Y);r_brother(Y, X).

brother(X,Y) :- s_brother(X, Y).
brother(X,Y) :- s_brother(X, Z),s_brother(Z, Y),X\=Y.

, X Y, , , .

X\= Y , "alin" .