  Cyber-physical systems of today are generating large volumes of time-series
data. As manual inspection of such data is not tractable, the need for learning
methods to help discover logical structure in the data has increased. We
propose a logic-based framework that allows domain-specific knowledge to be
embedded into formulas in a parametric logical specification over time-series
data. The key idea is to then map a time series to a surface in the parameter
space of the formula. Given this mapping, we identify the Hausdorff distance
between boundaries as a natural distance metric between two time-series data
under the lens of the parametric specification. This enables embedding
non-trivial domain-specific knowledge into the distance metric and then using
off-the-shelf machine learning tools to label the data. After labeling the
data, we demonstrate how to extract a logical specification for each label.
Finally, we showcase our technique on real world traffic data to learn
classifiers/monitors for slow-downs and traffic jams.
