Characterizing Consistency-Based Diagnoses

In this paper, we are mainly concerned with consistency-based diagnoses for systems represented in a propositional framework. Several characterizations of such diagnoses (mainly minimal diagnoses, kernel diagnoses, MT-diagnoses) have been proposed so far. Unfortunately, minimal diagnoses, and MT-diagnoses characterize only some consistency-based diagnoses and the set of kernel diagnoses for a system is often unsufficiently concise to be helpful; especially, the kernel diagnoses approach does not suggest any way to incorporate hierarchical relations between components within the diagnostic process. As an alternative to the kernel diagnoses characterization, we introduce the theory minimal conflicts for a system S. This characterization can be used to check whether a candidate diagnosis is a consistency-based (resp. a partial, a kernel) diagnosis for S in polynomial time. Additionally, it can be used to find out a consistency-based (resp. a partial, a kernel) diagnosis for S in polynomial time. Based on their theory prime implicates characterization, we show how theory minimal conflicts for S can be derived without requiring all the minimal conflicts of S to be generated.