# Interval Logic Tensor Networks

arXiv: https://arxiv.org/abs/2303.17892 · HTML: https://mlsanity.com/paper/2303.17892/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Faster-LTN: a neuro-symbolic, end-to-end object detection architecture](https://mlsanity.com/paper/2107.01877/) (2021)
- [Event Extraction: A Survey](https://mlsanity.com/paper/2210.03419/) (2022)
- [Using DeepProbLog to perform Complex Event Processing on an Audio Stream](https://mlsanity.com/paper/2110.08090/) (2021)

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

- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)

## Abstract (arXiv)

In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy logic, event durations using trapezoidal fuzzy intervals, and fuzzy temporal relations using relationships between the intervals' areas. We propose Interval Logic Tensor Networks (ILTN), a neuro-symbolic system that learns by propagating gradients through IRL. In order to support effective learning, ILTN defines smoothened versions of the fuzzy intervals and temporal relations of IRL using softplus activations. We show that ILTN can successfully leverage knowledge expressed in IRL in synthetic tasks that require reasoning about events to predict their fuzzy durations. Our results show that the system is capable of making events compliant with background temporal knowledge.