sLTN：结构逻辑张量网络

中文摘要 AI 辅助

逻辑张量网络（LTN）是一种神经符号框架，其中一阶逻辑通过张量运算进行解释，可将逻辑约束与可微学习相融合。但原始LTN公式主要适用于以个体的扁平集合表示的数据，未明确捕捉时间顺序、序列位置或图连接性等结构组织。本文提出sLTN，即LTN的扩展版本，它将结构维度作为语言的一等元素。结构维度表示与特定领域组织相关的命名张量轴，如时间步、序列位置或图节点，可被显式量化、通过结构关系关联，并直接在逻辑层面表达时间、序列和关系约束。本文对sLTN的语法和模糊张量语义进行了形式化，证明在无结构维度时，该框架会退化为原始LTN语义作为特例。此外，本文描述了基于声明式签名、公式解析和张量解释的PyTorch实现，并在代表性的时间和序列推理示例中对该框架进行了说明。本文是sltn库的配套论文，该库可在指定网址获取。

英文摘要

Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.

发表机构

• Nokia Bell Labs（诺基亚贝尔实验室）
• Fondazione Bruno Kessler（布鲁诺·凯塞勒基金会）

机构由 AI 辅助整理，请以论文原文为准。