  This paper presents a novel framework for inferring timed temporal logic
properties from data. The dataset comprises pairs of finite-time system traces
and corresponding labels, denoting whether the traces demonstrate specific
desired behaviors, e.g. whether the ship follows a safe route or not. Our
proposed approach leverages decision-tree-based methods to infer Signal
Temporal Logic classifiers using primitive formulae. We formulate the inference
process as a mixed integer linear programming optimization problem, recursively
generating constraints to determine both data classification and tree
structure. Applying a max-flow algorithm on the resultant tree transforms the
problem into a global optimization challenge, leading to improved
classification rates compared to prior methodologies. Moreover, we introduce a
technique to reduce the number of constraints by exploiting the symmetry
inherent in STL primitives, which enhances the algorithm's time performance and
interpretability. To assess our algorithm's effectiveness and classification
performance, we conduct three case studies involving two-class, multi-class,
and complex formula classification scenarios.
