transitive closure over a symmetric relation in prolog

Question

I am a prolog beginner and I want to create the \"brother\" relation.

The relation should be symmetric as in if brother(alin, alex) is true,

Answer 1

You can write the brother relation like this (exactly like the transitive definition)

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.

which mean X is brother of Y if he is a symmetric brother, or they have a brother in common, and add the condition that they are different.

try adding to X\=Y to your code to get rid of "alin" as a solution.

Answer 2

I think the basic problem is that you do not check if L2 is already found in the first clause of t_brother/3. And the initial L1 should be added to the list in brother/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]).

You can still shorten the solution by using a disjunction:

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