Counterfactual explanations suggest what should be different in the input instance to change the outcome of an AI system. When dealing with counterfactual explanations in the field of Predictive Process Monitoring, however, control flow relationships among events have to be carefully considered. A counterfactual, indeed, should not violate control flow relationships among activities (temporal background knowledege). Within the field of Explainability in Predictive Process Monitoring, there have been a series of works regarding counterfactual explanations for outcome-based predictions. However, none of them consider the inclusion of temporal background knowledge when generating these counterfactuals. In this work, we adapt state-of-the-art techniques for counterfactual generation in the domain of XAI that are based on genetic algorithms to consider a series of temporal constraints at runtime. We assume that this temporal background knowledge is given, and we adapt the fitness function, as well as the crossover and mutation operators, to maintain the satisfaction of the constraints. The proposed methods are evaluated with respect to state-of-the-art genetic algorithms for counterfactual generation and the results are presented. We showcase that the inclusion of temporal background knowledge allows the generation of counterfactuals more conformant to the temporal background knowledge, without however losing in terms of the counterfactual traditional quality metrics.
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