# Learning Temporal Logic Predicates from Data with Statistical Guarantees

arXiv: https://arxiv.org/abs/2406.10449 · HTML: https://mlsanity.com/paper/2406.10449/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 15 Jun 2024.

## Builds on (most cited first, 15 of 15)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Formal Specifications from Natural Language](https://mlsanity.com/paper/2206.01962/) (2022)
- [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Learning Interpretable Temporal Properties from Positive Examples Only](https://mlsanity.com/paper/2209.02650/) (2022)
- [A Robust Genetic Algorithm for Learning Temporal Specifications from Data](https://mlsanity.com/paper/1711.06202/) (2017)
- [Logic-based Clustering and Learning for Time-Series Data](https://mlsanity.com/paper/1612.07823/) (2016)
- [Interpretable Safety Validation for Autonomous Vehicles](https://mlsanity.com/paper/2004.06805/) (2020)
- [Satisfiability.jl: Satisfiability Modulo Theories in Julia](https://mlsanity.com/paper/2309.08778/) (2023)

## Built on by (most cited first, 3 of 3)

- [Conformal Prediction for Signal Temporal Logic Inference](https://mlsanity.com/paper/2509.25473/) (2025)
- [Conformalized Signal Temporal Logic Inference under Covariate Shift](https://mlsanity.com/paper/2603.27062/) (2026)
- [Class-Conditional Conformal Prediction for Signal Temporal Logic Inference with Many Classes](https://mlsanity.com/paper/2610.14352/) (2026)

## Abstract (arXiv)

Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining motion planning among autonomous agents, and classifying data. However, existing methods for learning temporal logic predicates from data do not provide assurances about the correctness of the resulting predicate. We present a novel method to learn temporal logic predicates from data with finite-sample correctness guarantees. Our approach leverages expression optimization and conformal prediction to learn predicates that correctly describe future trajectories under mild statistical assumptions. We provide experimental results showing the performance of our approach on a simulated trajectory dataset and perform ablation studies to understand how each component of our algorithm contributes to its performance.