  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.
