First-Order Temporal Logic Tensor Networks

• URL: http://arxiv.org/abs/2606.29972v1
• Date: Mon, 29 Jun 2026 08:48:23 GMT
• Title: First-Order Temporal Logic Tensor Networks
• Abstract summary: We present First-Order Temporal Logic Networks (FOT-LTN) that is an extension of Logic Networks (LTN)<n>In particular, FOT-LTN joins the syntax of First-Order Linear Temporal Logic with the fuzzy (and real-valued) semantics of LTN.<n>A first evaluation regards a temporal knowledge graph completion task on two synthetic datasets with respect to dedicated (purely neural) methods.
• Score: 47.56930079312276
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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