The task of decentralized decision-making involves interaction of a set of local decision-makers, each of which operates under limited sensing capabilities and is thus subjected to ambiguity during the process of decision-making. In our prior work, we made a key observation that such ambiguities are of differing gradations and presented a framework for inferencing over varying ambiguity levels to arrive at local and global control decisions. We develop a similar framework for performing diagnosis in a decentralized setting. For each event-trace executed by a system being monitored, each local diagnoser issues its own diagnosis decision (failure or nonfailure or unsure), tagged with a certain ambiguity level (zero being the minimum). A global diagnosis decision is taken to be a ldquowinningrdquo local diagnosis decision, i.e., one with a minimum ambiguity level. The computation of an ambiguity level for a local decision requires an assessment of the self-ambiguity as well as the ambiguities of the others, and an inference based up on such knowledge. In order to characterize the class of systems for which any fault can be detected within a uniformly bounded number of steps (or ldquodelayrdquo), we introduce the notion of N -inference-diagnosability for Failures (also called N-inference F-diagnosability), where the index N represents the maximum ambiguity level of any winning local decision. We show that the codiagnosability introduced in is the same as 0-inference F-diagnosability; the conditional F-codiagnosability introduced in , is a type of 1-inference F-diagnosability; the class of higher-index inference F-diagnosable systems strictly subsumes the class of lower-index ones; and the class of inference F-diagnosable systems is strictly subsumed by the class of systems that are centrally F-diagnosable.