First-Order Temporal Logic Tensor Networks

2026-06-29

AI Summary

Existing neuro-symbolic approaches struggle to effectively model first-order linear temporal logical reasoning involving the evolution of object attributes and relations over time. This work proposes the first end-to-end differentiable neuro-symbolic framework capable of handling quantified first-order linear temporal logic. By integrating Logic Tensor Networks with fuzzy real-valued semantics, the method enables a unified differentiable treatment of both temporal operators and quantificational structures. It thereby addresses a critical gap in differentiable neuro-symbolic modeling for dynamic knowledge reasoning. Empirical evaluation demonstrates that the proposed approach significantly outperforms specialized purely neural models on two synthetic temporal knowledge graph completion tasks.

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.

Problem

• neuro-symbolic AI
• temporal logic
• first-order logic
• time-varying relations
• differentiable reasoning

Innovation

• First-Order Temporal Logic
• Logic Tensor Networks
• Neuro-Symbolic AI
• Temporal Knowledge Graph
• Differentiable Reasoning