# Time Window Temporal Logic

arXiv: https://arxiv.org/abs/1602.04294 · HTML: https://mlsanity.com/paper/1602.04294/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2016.

## Built on by (most cited first, 4 of 4)

- [Reinforcement Learning Under Probabilistic Spatio-Temporal Constraints with Time Windows](https://mlsanity.com/paper/2307.15910/) (2023)
- [Probabilistic Satisfaction of Temporal Logic Constraints in Reinforcement Learning via Adaptive Policy-Switching](https://mlsanity.com/paper/2410.08022/) (2024)
- [Accelerating Proximal Policy Optimization Learning Using Task Prediction for Solving Environments with Delayed Rewards](https://mlsanity.com/paper/2411.17861/) (2024)
- [Hyperproperty-Constrained Secure Reinforcement Learning](https://mlsanity.com/paper/2508.00106/) (2025)

## Abstract (arXiv)

This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are typically seen in robotics and control applications. This paper also discusses the relaxation of TWTL formulae with respect to deadlines of tasks. Efficient automata-based frameworks to solve synthesis, verification and learning problems are also presented. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the specification. Case studies illustrating the expressivity of the logic and the proposed algorithms are included.