# Learning Linear Temporal Properties from Noisy Data: A MaxSAT Approach

arXiv: https://arxiv.org/abs/2104.15083 · HTML: https://mlsanity.com/paper/2104.15083/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Learning Linear Temporal Properties](https://mlsanity.com/paper/1806.03953/) (2018)
- [Mining Parametric Temporal Logic Properties in Model Based Design for Cyber-Physical Systems](https://mlsanity.com/paper/1512.07956/) (2015)
- [Information-Guided Temporal Logic Inference with Prior Knowledge](https://mlsanity.com/paper/1811.08846/) (2018)
- [Learning Interpretable Models in the Property Specification Language](https://mlsanity.com/paper/2002.03668/) (2020)
- [Interval Temporal Logic Decision Tree Learning](https://mlsanity.com/paper/2003.04952/) (2020)
- [Census Signal Temporal Logic Inference for Multi-Agent Group Behavior Analysis](https://mlsanity.com/paper/1610.05612/) (2016)
- [Graph Temporal Logic Inference for Classification and Identification](https://mlsanity.com/paper/1903.09714/) (2019)

## Built on by (most cited first, 11 of 11)

- [Scalable Anytime Algorithms for Learning Fragments of Linear Temporal Logic](https://mlsanity.com/paper/2110.06726/) (2021)
- [Differentiable Inference of Temporal Logic Formulas](https://mlsanity.com/paper/2208.05440/) (2022)
- [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)
- [Pointwise-in-Time Explanation for Linear Temporal Logic Rules](https://mlsanity.com/paper/2306.13956/) (2023)
- [On Generating Explanations for Reinforcement Learning Policies: An Empirical Study](https://mlsanity.com/paper/2309.16960/) (2023)
- [Learning to Estimate System Specifications in Linear Temporal Logic using Transformers and Mamba](https://mlsanity.com/paper/2405.20917/) (2024)
- [Symmetry Detection in Trajectory Data for More Meaningful Reinforcement Learning Representations](https://mlsanity.com/paper/2211.16381/) (2022)
- [Data-Driven Model Discrimination of Switched Nonlinear Systems with Temporal Logic Inference](https://mlsanity.com/paper/2306.09966/) (2023)
- [Learning Interpretable Classifiers for PDDL Planning](https://mlsanity.com/paper/2410.10011/) (2024)
- [Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons](https://mlsanity.com/paper/2505.18030/) (2025)

## Abstract (arXiv)

We address the problem of inferring descriptions of system behavior using Linear Temporal Logic (LTL) from a finite set of positive and negative examples. Most of the existing approaches for solving such a task rely on predefined templates for guiding the structure of the inferred formula. The approaches that can infer arbitrary LTL formulas, on the other hand, are not robust to noise in the data. To alleviate such limitations, we devise two algorithms for inferring concise LTL formulas even in the presence of noise. Our first algorithm infers minimal LTL formulas by reducing the inference problem to a problem in maximum satisfiability and then using off-the-shelf MaxSAT solvers to find a solution. To the best of our knowledge, we are the first to incorporate the usage of MaxSAT solvers for inferring formulas in LTL. Our second learning algorithm relies on the first algorithm to derive a decision tree over LTL formulas based on a decision tree learning algorithm. We have implemented both our algorithms and verified that our algorithms are efficient in extracting concise LTL descriptions even in the presence of noise.