# Interval Signal Temporal Logic from Natural Inclusion Functions

arXiv: https://arxiv.org/abs/2309.10686 · HTML: https://mlsanity.com/paper/2309.10686/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2023.

## Built on by (most cited first, 2 of 2)

- [Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations](https://mlsanity.com/paper/2605.13923/) (2026)
- [Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic](https://mlsanity.com/paper/2607.08899/) (2026)

## Abstract (arXiv)

We propose an interval extension of Signal Temporal Logic (STL) called Interval Signal Temporal Logic (ISTL). Given an STL formula, we consider an interval inclusion function for each of its predicates. Then, we use minimal inclusion functions for the min and max functions to recursively build an interval robustness that is a natural inclusion function for the robustness of the original STL formula. The resulting interval semantics accommodate, for example, uncertain signals modeled as a signal of intervals and uncertain predicates modeled with appropriate inclusion functions. In many cases, verification or synthesis algorithms developed for STL apply to ISTL with minimal theoretic and algorithmic changes, and existing code can be readily extended using interval arithmetic packages at negligible computational expense. To demonstrate ISTL, we present an example of offline monitoring from an uncertain signal trace obtained from a hardware experiment and an example of robust online control synthesis enforcing an STL formula with uncertain predicates.