# Learning Linear Temporal Properties

arXiv: https://arxiv.org/abs/1806.03953 · HTML: https://mlsanity.com/paper/1806.03953/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2018.

## Built on by (most cited first, 30 of 41)

- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [The Complexity of Learning Linear Temporal Formulas from Examples](https://mlsanity.com/paper/2102.00876/) (2021)
- [Learning Interpretable Temporal Properties from Positive Examples Only](https://mlsanity.com/paper/2209.02650/) (2022)
- [Learning Linear Temporal Properties from Noisy Data: A MaxSAT Approach](https://mlsanity.com/paper/2104.15083/) (2021)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [Scalable Anytime Algorithms for Learning Fragments of Linear Temporal Logic](https://mlsanity.com/paper/2110.06726/) (2021)
- [LTL learning on GPUs](https://mlsanity.com/paper/2402.12373/) (2024)
- [Learning Finite Linear Temporal Logic Specifications with a Specialized Neural Operator](https://mlsanity.com/paper/2111.04147/) (2021)
- [Testing learning-enabled cyber-physical systems with Large-Language Models: A Formal Approach](https://mlsanity.com/paper/2311.07377/) (2023)
- [Learning temporal formulas from examples is hard](https://mlsanity.com/paper/2312.16336/) (2023)
- [Uncertainty-Aware Signal Temporal Logic Inference](https://mlsanity.com/paper/2105.11545/) (2021)
- [Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic](https://mlsanity.com/paper/2310.17410/) (2023)
- [Learning Reward Machines from Partially Observed Policies](https://mlsanity.com/paper/2502.03762/) (2025)
- [Inferring Temporal Logic Properties from Data using Boosted Decision Trees](https://mlsanity.com/paper/2105.11508/) (2021)
- [Temporal and Object Quantification Networks](https://mlsanity.com/paper/2106.05891/) (2021)
- [Process discovery on deviant traces and other stranger things](https://mlsanity.com/paper/2109.14883/) (2021)
- [Learning Temporal Rules from Noisy Timeseries Data](https://mlsanity.com/paper/2202.05403/) (2022)
- [A Framework for Understanding and Visualizing Strategies of RL Agents](https://mlsanity.com/paper/2208.08552/) (2022)
- [Learning Probabilistic Temporal Logic Specifications for Stochastic Systems](https://mlsanity.com/paper/2505.12107/) (2025)
- [Learning Temporal Logic Properties: an Overview of Two Recent Methods](https://mlsanity.com/paper/2212.00916/) (2022)
- [Reverse Engineering of Temporal Queries Mediated by LTL Ontologies](https://mlsanity.com/paper/2305.01248/) (2023)
- [Pointwise-in-Time Explanation for Linear Temporal Logic Rules](https://mlsanity.com/paper/2306.13956/) (2023)
- [A Safe Preference Learning Approach for Personalization with Applications to Autonomous Vehicles](https://mlsanity.com/paper/2311.02099/) (2023)
- [Integrating Explanations in Learning LTL Specifications from Demonstrations](https://mlsanity.com/paper/2404.02872/) (2024)
- [Learning to Estimate System Specifications in Linear Temporal Logic using Transformers and Mamba](https://mlsanity.com/paper/2405.20917/) (2024)
- [SAT-Based Bounded Fitting for the Description Logic ALC](https://mlsanity.com/paper/2507.21752/) (2025)
- [LTLf Learning Meets Boolean Set Cover](https://mlsanity.com/paper/2509.24616/) (2025)
- [Time-Incremental Learning from Data Using Temporal Logics](https://mlsanity.com/paper/2112.14300/) (2021)
- [Specification sketching for Linear Temporal Logic](https://mlsanity.com/paper/2206.06722/) (2022)
- [Learning Probabilistic Temporal Safety Properties from Examples in Relational Domains](https://mlsanity.com/paper/2211.03461/) (2022)

## Abstract (arXiv)

We present two novel algorithms for learning formulas in Linear Temporal Logic (LTL) from examples. The first learning algorithm reduces the learning task to a series of satisfiability problems in propositional Boolean logic and produces a smallest LTL formula (in terms of the number of subformulas) that is consistent with the given data. Our second learning algorithm, on the other hand, combines the SAT-based learning algorithm with classical algorithms for learning decision trees. The result is a learning algorithm that scales to real-world scenarios with hundreds of examples, but can no longer guarantee to produce minimal consistent LTL formulas. We compare both learning algorithms and demonstrate their performance on a wide range of synthetic benchmarks. Additionally, we illustrate their usefulness on the task of understanding executions of a leader election protocol.