I get what you're trying to say, that in Prolog you are able to lookup structures by their shape, and not by some pre-defined path, as in other languages, so yo

I get what you're trying to say, that in Prolog you are able to lookup structures by their shape, and not by some pre-defined path, as in other languages, so you can do both `edge(1, A)` and `edge(A, 1)`. But the graph in your example is still directed, simply by the virtue of predicate arguments being ordered. So your example misses two rules to be correct. reachable(V, W) :- edge(V, W). reachable(V, W) :- edge(W, V). reachable(V, W) :- reachable(V, U), reachable(U, W). Alternatively you could introduce edge(V, W) :- edge(W, V).