T-ILR: a Neurosymbolic Integration for LTLf

2025-08-21

AI Summary

Existing approaches for integrating Linear Temporal Logic over finite traces (LTLf) specifications into deep learning require explicit construction of finite-state automata (FSA), limiting scalability and differentiability. This paper proposes T-ILR, the first end-to-end differentiable framework for embedding LTLf specifications directly into sequential learning tasks. T-ILR introduces a differentiable temporal constraint formulation grounded in fuzzy LTLf semantics and couples it with an Iterative Local Refinement (ILR) algorithm to enable neural-symbolic joint learning without FSA construction. Unlike conventional symbolic-neural hybrid methods, T-ILR supports full gradient propagation through temporal logic constraints, substantially reducing computational overhead. Empirical evaluation on image sequence classification demonstrates improved accuracy and faster convergence, validating T-ILR’s effectiveness, scalability, and practicality for modeling temporal domain knowledge.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Description Logics

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

State-of-the-art approaches for integrating symbolic knowledge with deep learning architectures have demonstrated promising results in static domains. However, methods to handle temporal logic specifications remain underexplored. The only existing approach relies on an explicit representation of a finite-state automaton corresponding to the temporal specification. Instead, we aim at proposing a neurosymbolic framework designed to incorporate temporal logic specifications, expressed in Linear Temporal Logic over finite traces (LTLf), directly into deep learning architectures for sequence-based tasks. We extend the Iterative Local Refinement (ILR) neurosymbolic algorithm, leveraging the recent introduction of fuzzy LTLf interpretations. We name this proposed method Temporal Iterative Local Refinement (T-ILR). We assess T-ILR on an existing benchmark for temporal neurosymbolic architectures, consisting of the classification of image sequences in the presence of temporal knowledge. The results demonstrate improved accuracy and computational efficiency compared to the state-of-the-art method.

Problem

• Integrating temporal logic specifications into deep learning architectures
• Handling Linear Temporal Logic over finite traces (LTLf)
• Improving accuracy and efficiency in sequence-based classification tasks

Innovation

• T-ILR neurosymbolic framework for LTLf
• Extends ILR with fuzzy LTLf interpretations
• Integrates temporal logic into deep learning