mlsanityData to 14 Oct 2026

Learning Probabilistic Temporal Logic Specifications for Stochastic Systems

arXiv 2505.12107 ↗First posted 17 May 2025cs.LO cs.AI cs.FLcited by 2

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Abstract (arXiv)

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly characterise systems with stochastic behaviour, which occur commonly in reinforcement learning and formal verification. We consider the passive learning problem of inferring a Boolean combination of probabilistic LTL (PLTL) formulas from a set of Markov chains, classified as either positive or negative. We propose a novel learning algorithm that infers concise PLTL specifications, leveraging grammar-based enumeration, search heuristics, probabilistic model checking and Boolean set-cover procedures. We demonstrate the effectiveness of our algorithm in two use cases: learning from policies induced by RL algorithms and learning from variants of a probabilistic model. In both cases, our method automatically and efficiently extracts PLTL specifications that succinctly characterise the temporal differences between the policies or model variants.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 20 of its 44 references that are in the map. First posted on arXiv 17 May 2025.

Builds on

20 of 44 references.

References · 20

  1. 2016OpenAI Gymcited by 1,736
  2. 2024Reinforcement learningcited by 247
  3. 2016Reinforcement Learning With Temporal Logic Rewardscited by 117
  4. 2019Reinforcement Learning for Temporal Logic Control Synthesis with Probabilistic Satisfaction Guaranteescited by 77
  5. 2019Control Synthesis from Linear Temporal Logic Specifications using Model-Free Reinforcement Learningcited by 75
  6. 2018Learning Linear Temporal Propertiescited by 41
  7. 2019Generation of Policy-Level Explanations for Reinforcement Learningcited by 37
  8. 2022From Spot 2.0 to Spot 2.10: What's New?cited by 22
  9. 2019Interpretable Classification of Time-Series Data using Efficient Enumerative Techniquescited by 20
  10. 2023Sample Efficient Model-free Reinforcement Learning from LTL Specifications with Optimality Guaranteescited by 18
  11. 2020Re-understanding Finite-State Representations of Recurrent Policy Networkscited by 15
  12. 2022Learning Interpretable Temporal Properties from Positive Examples Onlycited by 12
8 more
  1. 2017A Robust Genetic Algorithm for Learning Temporal Specifications from Datacited by 11
  2. 2020Learning Interpretable Models in the Property Specification Languagecited by 11
  3. 2021Scalable Anytime Algorithms for Learning Fragments of Linear Temporal Logiccited by 9
  4. 2023Explainable Multi-Agent Reinforcement Learning for Temporal Queriescited by 9
  5. 2024LTL learning on GPUscited by 6
  6. 2022Differentiable Inference of Temporal Logic Formulascited by 5
  7. 2024SAT-based Learning of Computation Tree Logiccited by 4
  8. 2024Learning Branching-Time Properties in CTL and ATL via Constraint Solvingcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025LTLf Learning Meets Boolean Set Covercited by 1
  2. 2026SpecRLBench: A Benchmark for Generalization in Specification-Guided Reinforcement Learningcited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2024Probabilistic Model Checking of Stochastic Reinforcement Learning Policies
  2. 2024DeepLTL: Learning to Efficiently Satisfy Complex LTL Specifications for Multi-Task RL
  3. 2024Regret-Free Reinforcement Learning for LTL Specifications
  4. 2025Accelerated Learning with Linear Temporal Logic using Differentiable Simulation
  5. 2024Directed Exploration in Reinforcement Learning from Linear Temporal Logic
  6. 2024Comp-LTL: Temporal Logic Planning via Zero-Shot Policy Composition
  7. 2024Probabilistic Satisfaction of Temporal Logic Constraints in Reinforcement Learning via Adaptive Policy-Switching
  8. 2026Integrating LTL Constraints into PPO for Safe Reinforcement Learning