My prof. said that using the language of definite programs, it is not possible to construct contradictory descriptions, i.e. unsatisfiable sets of formulas.
However, since a definite program can consist in only one clause. We can take the clause $p(x)$. Now, if $p(x)$ is false for every object of every domain, this clause is unsatisfiable. Am i wrong ?
A single clause (i.e. an atomic formula) $p(x)$ cannot be unsatisfiable.
We can interpret it in the domain $\mathbb N$ and interpret $x$ as $2$ and $p(x)$ as "$x$ is even".