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 a prior work (Kumar and Takai, 2005) we made an observation that such ambiguities are of differing gradations and presented a framework for inferencing over various local control decisions of varying ambiguity levels to arrive at a global control decision. A similar inferencing-based framework for the management of ambiguities in the decentralized diagnosis of failures was reported in Kumar and Takai (2006). The present paper extends this to the decentralized diagnosis of nonfailures which requires that any ambiguity about the non-occurrence of a failure be resolved within a uniformly bounded delay. As shown in this paper, the decentralized diagnosability for failures does not imply that for nonfailures, and vice-versa.