# First-Order Temporal Logic Tensor Networks

arXiv: https://arxiv.org/abs/2606.29972 · HTML: https://mlsanity.com/paper/2606.29972/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Heterogeneous Temporal Graph Neural Network](https://mlsanity.com/paper/2110.13889/) (2021)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [TLINet: Differentiable Neural Network Temporal Logic Inference](https://mlsanity.com/paper/2405.06670/) (2024)
- [Neuro-Symbolic Predictive Process Monitoring](https://mlsanity.com/paper/2509.00834/) (2025)
- [ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Search](https://mlsanity.com/paper/2506.09701/) (2025)
- [T-ILR: a Neurosymbolic Integration for LTLf](https://mlsanity.com/paper/2508.15943/) (2025)
- [A Neuro-Symbolic Framework for Sequence Classification with Relational and Temporal Knowledge](https://mlsanity.com/paper/2505.05106/) (2025)
- [First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications](https://mlsanity.com/paper/2202.00610/) (2022)
- [Interval Logic Tensor Networks](https://mlsanity.com/paper/2303.17892/) (2023)

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

- [sLTN: Structural Logic Tensor Networks](https://mlsanity.com/paper/2608.11136/) (2026)

## Abstract (arXiv)

Most of the existing neuro-symbolic AI methods focus on the scenario of static knowledge where objects do not change according to a temporal dimension. Temporal neuro-symbolic works are still under explored and are mainly developed for time-interval logic or propositional linear temporal logic. There is a lack of models studying linear temporal logics with predicates that deal with objects whose properties and relations change through the time. We present First-Order Temporal Logic Tensor Networks (FOT-LTN) that is an extension of Logic Tensor Networks (LTN) that fills this gap by considering a linear-temporal dimension. In particular, FOT-LTN joins the syntax of First-Order Linear Temporal Logic with the fuzzy (and real-valued) semantics of LTN obtaining a framework that supports both temporal operators and quantifiers and is totally differentiable. A first evaluation regards a temporal knowledge graph completion task on two synthetic datasets showing better performance of FOT-LTN with respect to dedicated (purely neural) methods.