English

First-Order Temporal Logic Tensor Networks

Artificial Intelligence 2026-06-29 v1 Machine Learning Logic in Computer Science

Abstract

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.

Cite

@article{arxiv.2606.29972,
  title  = {First-Order Temporal Logic Tensor Networks},
  author = {Luca Boscarato and Ivan Donadello and Alessandro Artale and Marco Montali and Fabrizio Maria Maggi},
  journal= {arXiv preprint arXiv:2606.29972},
  year   = {2026}
}