  Answer set programs used in real-world applications often require that the
program is usable with different input data. This, however, can often lead to
contradictory statements and consequently to an inconsistent program. Causes
for potential contradictions in a program are conflicting rules. In this paper,
we show how to ensure that a program $\mathcal{P}$ remains non-contradictory
given any allowed set of such input data. For that, we introduce the notion of
conflict-resolving $\lambda$- extensions. A conflict-resolving
$\lambda$-extension for a conflicting rule $r$ is a set $\lambda$ of (default)
literals such that extending the body of $r$ by $\lambda$ resolves all
conflicts of $r$ at once. We investigate the properties that suitable
$\lambda$-extensions should possess and building on that, we develop a strategy
to compute all such conflict-resolving $\lambda$-extensions for each
conflicting rule in $\mathcal{P}$. We show that by implementing a conflict
resolution process that successively resolves conflicts using
$\lambda$-extensions eventually yields a program that remains non-contradictory
given any allowed set of input data.
