Model-based diagnosis of discrete-event systems (DESs) generates a set of candidates upon the reception of a temporal observation. In the literature, a candidate is a set of faults produced by a trajectory of the DES that is consistent with the temporal observation. As such, a candidate does not convey any temporal relationship between faults, nor does it account for multiple occurrences of the same fault. To overcome the limitations of this set-oriented approach to diagnosis of DESs, the novel notions of temporal fault and temporal diagnosis are proposed, along with two diagnosis techniques. A temporal fault is the (possibly unbounded) sequence of faults produced by a trajectory. A temporal diagnosis is a (possibly infinite) set of temporal faults. Hence, in this new temporal-oriented approach to diagnosis of DESs, a candidate is a temporal fault. The fact that a temporal diagnosis turns out to be a regular language is key to coping with the infinity of candidates, which can be represented by a regular expression. The diagnosis task can be performed either by restricting the DES space to the trajectories that are consistent with the temporal observation, or by exploiting a temporal diagnoser which allows for fast online diagnosis. The claim of this paper is that the extra temporal information embedded in candidates may be essential in taking critical decisions based on the diagnosis results.

Since its appearance in AI, model-based diagnosis is intrinsically set-oriented. Given a sequence of observations, the diagnosis task generates a set of diagnoses, or candidates, each candidate complying with the observations. What all the approaches in the literature have in common is that a candidate is invariably a set of faulty elements (components, events, or otherwise). In this paper, we consider a posteriori diagnosis of discrete-event systems (DESs), which are described by networks of components that are modeled as communicating automata. The diagnosis problem consists in generating the candidates involved in the trajectories of the DES that conform with a given temporal observation. Oddly, in the literature on diagnosis of DESs, a candidate is still a set of faulty events, despite the temporal dimension of trajectories. In our view, when dealing with critical domains, such as power networks or nuclear plants, set-oriented diagnosis may be less than optimal in explaining the supposedly abnormal behavior of the DES, owing to the lack of any temporal information relevant to faults, along with the inability to discriminate between single and multiple occurrences of the same fault. Embedding temporal information in candidates may be essential for critical-decision making. This is why a temporal-oriented approach is proposed for diagnosis of DESs, where candidates are sequences of faults. This novel perspective comes with the burden of unbounded candidates and infinite collections of candidates, though. To cope with, a notation based on regular expressions on faults is adopted. The diagnosis task is supported by a temporal diagnoser, a flexible data structure that can grow over time based on new observations and domain-dependent scenarios.

Model-based diagnosis is typically set-oriented. In static systems, such as combinational circuits, a candidate (or diagnosis) is a set of faulty components that explains a set of observations. In discrete-event systems (DESs), a candidate is a set of faulty events occurring in a sequence of state changes that conforms with a sequence of observations. Invariably, a candidate is a set. This set-oriented perspective makes diagnosis of DESs narrow in explainability, owing to the lack of any temporal knowledge relevant to the faults within a candidate, along with the inability to discriminate between single and multiple occurrences of the same fault. Embedding temporal knowledge in a candidate, such as the relative temporal ordering of faults and the multiplicity of the same fault, may be essential for critical decision making. To favor explainability, the notions of temporal fault, explanation, and explainer are introduced in diagnosis of DESs. The explanation engine reacts to a given sequence of observations by generating and refining in real-time a sequence of regular expressions, where the language of each expression is a set of temporal faults. Moreover, to avoid total knowledge compilation, the explainer can be generated incrementally either offline, based on meaningful behavioral scenarios, or online, when being operated in solving specific diagnosis problems.