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This paper provides a new definition of diagnosability, that allows one to check the diagnosability of any set of system states, and by extension of properties that depend on the system state. The existing definitions and approaches for checking diagnosability apply to faults or sets of faults, and comparison shows that the new definition generalizes the existing ones. This new definition is applied to repair preconditions, and an example shows how this brings complementary information compared to classical fault diagnosability.
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