We propose a theory of abstraction of discrete-event systems (DES) formulated at the semantic level, i.e., as a function that maps event traces at the original (ground) level to traces at the abstract level. We study how diagnosis of DES can be performed using an abstract model, and under which conditions this process leads to a correct solution (i.e., a set of alternative diagnoses that include the real status of the system). Finally, we study how the use of an abstract model can affect the precision of diagnosis, i.e., the presence of spurious system states in the solution. To this end, we introduce the notion of diagnosability with abstract models, which ensures the precision of abstract diagnoses, and we discuss a practical way to test it.
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