# Specifying User Preferences using Weighted Signal Temporal Logic

arXiv: https://arxiv.org/abs/2010.00752 · HTML: https://mlsanity.com/paper/2010.00752/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 22 of 22)

- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Classification of Time-Series Data Using Boosted Decision Trees](https://mlsanity.com/paper/2110.00581/) (2021)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Neuro-symbolic Models for Interpretable Time Series Classification using Temporal Logic Description](https://mlsanity.com/paper/2209.09114/) (2022)
- [Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles](https://mlsanity.com/paper/2212.03323/) (2022)
- [Neural Network for Weighted Signal Temporal Logic](https://mlsanity.com/paper/2104.05435/) (2021)
- [Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networks](https://mlsanity.com/paper/2109.08078/) (2021)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)
- [Probabilistic Planning with Partially Ordered Preferences over Temporal Goals](https://mlsanity.com/paper/2209.12267/) (2022)
- [Inferring Temporal Logic Properties from Data using Boosted Decision Trees](https://mlsanity.com/paper/2105.11508/) (2021)
- [Probabilistic Planning with Prioritized Preferences over Temporal Logic Objectives](https://mlsanity.com/paper/2304.11641/) (2023)
- [Optimal Cost-Preference Trade-off Planning with Multiple Temporal Tasks](https://mlsanity.com/paper/2306.13222/) (2023)
- [Multi-Objective Controller Synthesis with Uncertain Human Preferences](https://mlsanity.com/paper/2105.04662/) (2021)
- [Learning Spatio-Temporal Specifications for Dynamical Systems](https://mlsanity.com/paper/2112.10714/) (2021)
- [Opportunistic Qualitative Planning in Stochastic Systems with Incomplete Preferences over Reachability Objectives](https://mlsanity.com/paper/2210.01878/) (2022)
- [A Safe Preference Learning Approach for Personalization with Applications to Autonomous Vehicles](https://mlsanity.com/paper/2311.02099/) (2023)
- [Reinforcement Learning Agent Training with Goals for Real World Tasks](https://mlsanity.com/paper/2107.10390/) (2021)
- [Time-Incremental Learning from Data Using Temporal Logics](https://mlsanity.com/paper/2112.14300/) (2021)
- [Preference-Based Planning in Stochastic Environments: From Partially-Ordered Temporal Goals to Most Preferred Policies](https://mlsanity.com/paper/2403.18212/) (2024)
- [Closing the Intent-to-Behavior Gap via Fulfillment Priority Logic](https://mlsanity.com/paper/2503.05818/) (2025)
- [Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons](https://mlsanity.com/paper/2505.18030/) (2025)
- [TimeSliver : Symbolic-Linear Decomposition for Explainable Time Series Classification](https://mlsanity.com/paper/2601.21289/) (2026)

## Abstract (arXiv)

We extend Signal Temporal Logic (STL) to enable the specification of importance and priorities. The extension, called Weighted STL (wSTL), has the same qualitative (Boolean) semantics as STL, but additionally defines weights associated with Boolean and temporal operators that modulate its quantitative semantics (robustness). We show that the robustness of wSTL can be defined as weighted generalizations of all known compatible robustness functionals (i.e., robustness scores that are recursively defined over formulae) that can take into account the weights in wSTL formulae. We utilize this weighted robustness to distinguish signals with respect to a desired wSTL formula that has sub-formulae with different importance or priorities and time preferences, and demonstrate its usefulness in problems with conflicting tasks where satisfaction of all tasks cannot be achieved. We also employ wSTL robustness in an optimization framework to synthesize controllers that maximize satisfaction of a specification with user specified preferences.