# Time Series Learning using Monotonic Logical Properties

arXiv: https://arxiv.org/abs/1802.08924 · HTML: https://mlsanity.com/paper/1802.08924/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Mining Interpretable Spatio-temporal Logic Properties for Spatially Distributed Systems](https://mlsanity.com/paper/2106.08548/) (2021)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)

## Abstract (arXiv)

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.