# Learning Interpretable Temporal Properties from Positive Examples Only

arXiv: https://arxiv.org/abs/2209.02650 · HTML: https://mlsanity.com/paper/2209.02650/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Extracting Automata from Recurrent Neural Networks Using Queries and Counterexamples](https://mlsanity.com/paper/1711.09576/) (2017)
- [Learning Linear Temporal Properties](https://mlsanity.com/paper/1806.03953/) (2018)
- [Symbolic LTLf Synthesis](https://mlsanity.com/paper/1705.08426/) (2017)
- [Interpretable Sequence Classification via Discrete Optimization](https://mlsanity.com/paper/2010.02819/) (2020)
- [Active Task-Inference-Guided Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2001.09227/) (2020)
- [Efficient, Safe, and Probably Approximately Complete Learning of Action Models](https://mlsanity.com/paper/1705.08961/) (2017)
- [Interpretable Apprenticeship Learning with Temporal Logic Specifications](https://mlsanity.com/paper/1710.10532/) (2017)
- [Information-Guided Temporal Logic Inference with Prior Knowledge](https://mlsanity.com/paper/1811.08846/) (2018)
- [Explaining Multi-stage Tasks by Learning Temporal Logic Formulas from Suboptimal Demonstrations](https://mlsanity.com/paper/2006.02411/) (2020)
- [Learning Interpretable Models in the Property Specification Language](https://mlsanity.com/paper/2002.03668/) (2020)
- [Scalable Anytime Algorithms for Learning Fragments of Linear Temporal Logic](https://mlsanity.com/paper/2110.06726/) (2021)
- [Planning with Incomplete Information in Quantified Answer Set Programming](https://mlsanity.com/paper/2108.06405/) (2021)
- [Graph Temporal Logic Inference for Classification and Identification](https://mlsanity.com/paper/1903.09714/) (2019)

## Built on by (most cited first, 12 of 12)

- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)
- [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)
- [Pointwise-in-Time Explanation for Linear Temporal Logic Rules](https://mlsanity.com/paper/2306.13956/) (2023)
- [Integrating Explanations in Learning LTL Specifications from Demonstrations](https://mlsanity.com/paper/2404.02872/) (2024)
- [Extracting Explainable Dates From Medical Images By Reverse-Engineering UNIX Timestamps](https://mlsanity.com/paper/2505.11451/) (2025)
- [SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specifications](https://mlsanity.com/paper/2608.05439/) (2026)
- [Data-Driven Model Discrimination of Switched Nonlinear Systems with Temporal Logic Inference](https://mlsanity.com/paper/2306.09966/) (2023)
- [Learning Tree Pattern Transformations](https://mlsanity.com/paper/2410.07708/) (2024)
- [Seqret: Mining Rule Sets from Event Sequences](https://mlsanity.com/paper/2505.06049/) (2025)
- [Active Learning of Symbolic Automata Over Rational Numbers](https://mlsanity.com/paper/2511.12315/) (2025)
- [On Synthesis of Metric Interval Temporal Logics](https://mlsanity.com/paper/2609.01032/) (2026)

## Abstract (arXiv)

We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. To this end, based on recent research trends, we rely on the fundamental yet interpretable models of deterministic finite automata (DFAs) and linear temporal logic (LTL) formulas. In contrast to most existing works for learning DFAs and LTL formulas, we rely on only positive examples. Our motivation is that negative examples are generally difficult to observe, in particular, from black-box systems. To learn meaningful models from positive examples only, we design algorithms that rely on conciseness and language minimality of models as regularizers. To this end, our algorithms adopt two approaches: a symbolic and a counterexample-guided one. While the symbolic approach exploits an efficient encoding of language minimality as a constraint satisfaction problem, the counterexample-guided one relies on generating suitable negative examples to prune the search. Both the approaches provide us with effective algorithms with theoretical guarantees on the learned models. To assess the effectiveness of our algorithms, we evaluate all of them on synthetic data.