Is "undecidable" can be represented in ASP (Answer Set Programming)?

Question

A sentence like

If a(X), then one can't decide/conclude anything about a(X) being b(X)

First attempt

b(X) | -b(X) :- a(X).

Second attempt

:- a(X), b(X).
:- a(X), -b(X).

First one makes no change to the solution while second one makes everything unsatisfiable.

Answer 1

After a long meditation, I will answer my own question...

One way to translate the sentence is

b(X) :- a(X), not -b(X).
-b(X) :- a(X), not b(X).