# T-ILR: a Neurosymbolic Integration for LTLf

arXiv: https://arxiv.org/abs/2508.15943 · HTML: https://mlsanity.com/paper/2508.15943/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Multi-Label Classification Neural Networks with Hard Logical Constraints](https://mlsanity.com/paper/2103.13427/) (2021)
- [Refining neural network predictions using background knowledge](https://mlsanity.com/paper/2206.04976/) (2022)
- [DeepDFA: Automata Learning through Neural Probabilistic Relaxations](https://mlsanity.com/paper/2408.08622/) (2024)
- [Conformance Checking of Fuzzy Logs against Declarative Temporal Specifications](https://mlsanity.com/paper/2406.12078/) (2024)
- [Knowledge Enhanced Neural Networks for relational domains](https://mlsanity.com/paper/2205.15762/) (2022)

## Built on by (most cited first, 3 of 3)

- [Grounding LTL Tasks in Sub-Symbolic RL Environments for Zero-Shot Generalization](https://mlsanity.com/paper/2602.09761/) (2026)
- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)
- [Neurosymbolic Learning of Interpretable World Models](https://mlsanity.com/paper/2610.19955/) (2026)

## Abstract (arXiv)

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only existing approach relies on an explicit representation of a finite-state automaton corresponding to the temporal specification. Instead, we aim at proposing a neurosymbolic framework designed to incorporate temporal logic specifications, expressed in Linear Temporal Logic over finite traces (LTLf), directly into deep learning architectures for sequence-based tasks. We extend the Iterative Local Refinement (ILR) neurosymbolic algorithm, leveraging the recent introduction of fuzzy LTLf interpretations. We name this proposed method Temporal Iterative Local Refinement (T-ILR). We assess T-ILR on an existing benchmark for temporal neurosymbolic architectures, consisting of the classification of image sequences in the presence of temporal knowledge. The results demonstrate improved accuracy and computational efficiency compared to the state-of-the-art method.