Offline and Online Learning of Signal Temporal Logic Formulae Using Decision Trees

In this article, we focus on inferring high-level descriptions of a system from its execution traces. Specifically, we consider a classification problem where system behaviors are described using formulae of Signal Temporal Logic (STL). Given a finite set of pairs of system traces and labels, where each label indicates whether the corresponding trace exhibits some system property, we devised a decision-tree-based framework that outputs an STL formula that can distinguish the traces. We also extend this approach to the online learning scenario. In this setting, it is assumed that new signals may arrive over time and the previously inferred formula should be updated to accommodate the new data. The proposed approach presents some advantages over traditional machine learning classifiers. In particular, the produced formulae are interpretable and can be used in other phases of the system’s operation, such as monitoring and control. We present two case studies to illustrate the effectiveness of the proposed algorithms: (1) a fault detection problem in an automotive system and (2) an anomaly detection problem in a maritime environment.