Learning Linear Temporal Specifications from Demonstrations with Uncertainty

2026-07-12

AI Summary

This work proposes a novel approach to learning Linear Temporal Logic (LTL) specifications from noisy demonstrations, explicitly accounting for trajectory uncertainty arising from sensor faults, measurement errors, or missing data. The method models uncertainty by defining a set of plausible trajectories around each observed trace using Hamming distance and introduces grouping constraints that require at least one trajectory per group to satisfy the learned LTL formula. This formulation is cast as a pseudo-Boolean optimization problem. By directly incorporating trajectory uncertainty into the learning process, the approach overcomes the limitations of conventional methods that assume either perfectly accurate demonstrations or only tolerate classification errors. Experimental results demonstrate significantly improved accuracy in recovering correct LTL specifications from uncertain demonstration data.

Abstract

Learning temporal logic specifications from system demonstrations is essential for tasks such as formal verification and controller synthesis, especially in safety-critical domains. Existing approaches typically assume demonstrations are correct or only affected by misclassification errors. In practice, however, system traces are often uncertain or incomplete due to sensor faults, measurement errors, or data loss. We present a framework for learning minimal Linear Temporal Logic (LTL) formulas from demonstrations with uncertainty. Our approach models uncertainty via Hamming distance to generate possible estimates around each observed trace, which are grouped with constraints requiring that at least one trace per group is consistent with the learned formula. Our problem is then reduced to an equivalent Pseudo-Boolean Optimization. We evaluate our method against state-of-the-art LTL learning approaches and show that it recovers specifications that more closely align with ground-truth formulas under uncertainty.

Problem

• Linear Temporal Logic
• uncertain demonstrations
• specification learning
• system traces
• temporal logic synthesis

Innovation

• Linear Temporal Logic
• Uncertainty Modeling
• Hamming Distance
• Pseudo-Boolean Optimization
• Specification Learning