# Robustness Measures and Monitors for Time Window Temporal Logic

arXiv: https://arxiv.org/abs/2304.06645 · HTML: https://mlsanity.com/paper/2304.06645/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Accelerating Proximal Policy Optimization Learning Using Task Prediction for Solving Environments with Delayed Rewards](https://mlsanity.com/paper/2411.17861/) (2024)

## Abstract (arXiv)

Temporal logics (TLs) have been widely used to formalize interpretable tasks for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently proposed as a specification language for dynamical systems. In particular, it can easily express robotic tasks, and it allows for efficient, automata-based verification and synthesis of control policies for such systems. In this paper, we define two quantitative semantics for this logic, and two corresponding monitoring algorithms, which allow for real-time quantification of satisfaction of formulas by trajectories of discrete-time systems. We demonstrate the new semantics and their runtime monitors on numerical examples.