This paper presents a formal framework for diagnosis. We focus on diagnosis from first principles, and study how the measurements affect diagnosis set. We explore the idea that the measurements do not eliminate an actual diagnosis from Diag (a set of diagnoses of a system being modeled). The measurements reduce the total diagnosis set, but in the case of minimal or kernel diagnoses it proves to be wrong: the sets of minimal diagnoses and kernel diagnoses do not have fixed points. In this paper we examine the notion of actual diagnosis abnormal components of which are preserved in the case of possible measurements. To get an actual diagnosis for the given system we use structural decomposition of the system in such a way that each diagnosis for the system is the product of local diagnosis for subsystems. We propose a formal algorithm which is capable to compute multiple fault diagnoses confirming the results of all the possible measurements. We also describe a class of systems having unique actual diagnosis.
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