On Establishing Robust Consistency in Answer Set Programs

Abstract: 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.