# sLTN: Structural Logic Tensor Networks

arXiv: https://arxiv.org/abs/2608.11136 · HTML: https://mlsanity.com/paper/2608.11136/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [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)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Integrating Learning and Reasoning with Deep Logic Models](https://mlsanity.com/paper/1901.04195/) (2019)
- [Neuro-Symbolic Artificial Intelligence: Towards Improving the Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2508.13678/) (2025)
- [Squareplus: A Softplus-Like Algebraic Rectifier](https://mlsanity.com/paper/2112.11687/) (2021)
- [Jacobian Descent for Multi-Objective Optimization](https://mlsanity.com/paper/2406.16232/) (2024)
- [Compensating Supervision Incompleteness with Prior Knowledge in Semantic Image Interpretation](https://mlsanity.com/paper/1910.00462/) (2019)
- [LTNtorch: PyTorch Implementation of Logic Tensor Networks](https://mlsanity.com/paper/2409.16045/) (2024)
- [Logic Tensor Network-Enhanced Generative Adversarial Network](https://mlsanity.com/paper/2601.03839/) (2026)
- [OntoMedRec: Logically-Pretrained Model-Agnostic Ontology Encoders for Medication Recommendation](https://mlsanity.com/paper/2401.15814/) (2024)
- [Integrating Background Knowledge in Medical Semantic Segmentation with Logic Tensor Networks](https://mlsanity.com/paper/2509.22399/) (2025)
- [Neuro-Symbolic Process Anomaly Detection](https://mlsanity.com/paper/2603.26461/) (2026)
- [Neuro-Symbolic Learning for Predictive Process Monitoring via Two-Stage Logic Tensor Networks with Rule Pruning](https://mlsanity.com/paper/2603.26944/) (2026)
- [From Large Language Model Predicates to Logic Tensor Networks: Neurosymbolic Offer Validation in Regulated Procurement](https://mlsanity.com/paper/2604.05539/) (2026)
- [Weakly Supervised Segmentation as Semantic-Based Regularization](https://mlsanity.com/paper/2605.13674/) (2026)
- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)

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

- [Auto-Formalizing Neuro-Symbolic Predictors](https://mlsanity.com/paper/2610.01519/) (2026)

## Abstract (arXiv)

Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.