推理时刻：基于模糊语义的LTLf可扩展神经符号学习

中文摘要 AI 辅助

神经符号（NeSy）人工智能旨在将深度学习（DL）架构与符号推理相融合。早期神经符号方法主要针对命题逻辑和一阶逻辑中的符号推理，近期研究已开始构建针对时态逻辑、特别是LTLf的神经符号框架。这些方法已确立时态神经符号为有前景的研究方向，为时态约束下的学习奠定了基础，但仍留下诸多未解决的问题。从理论角度，虽已提出多种用于解释LTLf的可微语义，但尚未在统一框架内进行正式且系统的定义；此外，现有方法通常依赖自动机表示时态知识，导致可扩展性受限。受此研究缺口驱动，本文作出以下贡献：（i）正式定义LTLf的不同模糊语义，并系统分析时态算子的等价性与对偶性相关理论性质；（ii）展示这些语义如何直接集成到名为DiffLTLf的新型神经符号框架中，无需依赖自动机即可实现灵活且可扩展的学习；（iii）引入比现有基准更复杂的新型学习任务评估协议。我们的结果表明，模糊语义的选择对预测性能有显著影响；此外，DiffLTLf的性能与最先进的概率方法相当，有时甚至更优，同时大幅提升了可扩展性。综上，这些结果确立了直接模糊解释是现有时态神经符号框架的具有竞争力且可扩展的替代方案。

英文摘要

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.

发表机构

• Fondazione Bruno Kessler（布鲁诺·凯塞勒基金会）
• Free University of Bozen-Bolzano（波尔扎诺自由大学）
• Università di Bologna（博洛尼亚大学）

机构由 AI 辅助整理，请以论文原文为准。