Time to Reason: Scalable Neurosymbolic Learning for LTLf via Fuzzy Semantics
2026-08-17 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors explore ways to combine deep learning with reasoning about things that happen over time, focusing on a specific type of logic called LTLf. They point out that previous methods used automata (state machines), which limits how well these methods scale to bigger problems. To address this, they define new fuzzy logic rules for LTLf and create a new framework called DiffLTLf that learns more flexibly without using automata. Their tests show that DiffLTLf is scalable and performs as well or better than current methods, and that the way fuzzy logic is set up really affects how well the model predicts.
Neurosymbolic AIDeep LearningTemporal LogicLTLf (Linear Temporal Logic on Finite Traces)Fuzzy SemanticsAutomataSymbolic ReasoningDifferentiable SemanticsScalabilityPredictive Performance
Authors
Riccardo Andreoni, Andrei Buliga, Alessandro Daniele, Paolo Felli, Chiara Ghidini, Marco Montali, Massimiliano Ronzani
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.