Time to Reason: Scalable Neurosymbolic Learning for LTLf via Fuzzy Semantics

2026-08-17

AI Summary

This study addresses the limitations of existing neuro-symbolic approaches for Linear Temporal Logic over finite traces (LTLf), which lack unified differentiable semantics and suffer from poor scalability due to automaton dependence. We propose DiffLTLf, a novel framework that formalizes fuzzy semantics for LTLf and exploits operator duality to establish an automaton-free differentiable neuro-symbolic learning paradigm alongside a high-complexity evaluation protocol. Experimental results demonstrate that fuzzy semantics significantly influence model performance. Furthermore, DiffLTLf matches or surpasses state-of-the-art probabilistic methods while substantially improving scalability. Consequently, this work provides an efficient and unified solution for neuro-symbolic learning with temporal logic, overcoming critical bottlenecks in current methodologies.

Abstract

Neurosymbolic (NeSy) Artificial Intelligence aims to integrate Deep Learning (DL) architectures with symbolic reasoning. While initial NeSy approaches have targeted mainly symbolic reasoning in propositional and first-order logics, recent works have started to address the construction of neurosymbolic frameworks for Temporal Logics, and in particular for LTLf. These approaches have established temporal NeSy as a promising research direction, laying the foundations for learning under temporal constraints. Nonetheless, they leave many questions unanswered. From a theoretical perspective, several differentiable semantics for interpreting LTLf have been proposed but have not yet been formally and systematically defined within a unified framework. Moreover, existing approaches commonly rely on automata to represent temporal knowledge, resulting in limited scalability. Motivated by this research gap, this paper provides the following contributions: (i) formally defining different fuzzy semantics for LTLf, and systematically analysing theoretical properties regarding equivalences and dualities of temporal operators; (ii) showing how these semantics can be directly integrated within a novel NeSy framework, called DiffLTLf, enabling flexible and scalable learning without relying on the usage of automata; and (iii) introducing a novel evaluation protocol of increased complexity of learning tasks w.r.t. existing benchmarks. Our results show that the choice of fuzzy semantics has a significant impact on predictive performance. Moreover, DiffLTLf achieves performance on par with, and sometimes superior to, state-of-the-art probabilistic approaches while substantially improving scalability. Taken together, these results establish direct fuzzy interpretations as a competitive and scalable alternative to existing temporal NeSy frameworks.

Problem

• Neurosymbolic AI
• LTLf
• Scalability
• Fuzzy Semantics
• Automata

Innovation

• Neurosymbolic AI
• LTLf
• Fuzzy Semantics
• DiffLTLf
• Scalability