sLTN: Structural Logic Tensor Networks

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Davide Rinaldi, Luciano Serafini
• Venue: arXiv: cs.AI
• Published: 2026-08-11
• Collected: 2026-08-12
• URL: http://arxiv.org/abs/2608.11136v1
• PDF: https://arxiv.org/pdf/2608.11136v1
• DOI: UNKNOWN
• Registry group: academic_apis_and_preprints
• Evidence role: canonical_academic_index
• Language: en
• Country / region: UNKNOWN

Plain-Language Brief

The paper introduces sLTN, an extension of Logic Tensor Networks (LTN), which is a neurosymbolic framework that combines first-order logic with tensor operations for differentiable learning. The new version can handle structural organization like temporal order, sequential position, or graph connectivity, and it recovers the original LTN semantics when no structural dimensions are present.

What the Document Says

• The paper discusses sLTN, an extension of LTN.
• sLTN is a neurosymbolic framework that combines first-order logic and tensor operations for differentiable learning.
• sLTN can handle structural organization such as temporal order, sequential position, or graph connectivity.
• When no structural dimensions are present, sLTN recovers the original LTN semantics.

Key Concepts Mentioned

• Logic Tensor Networks (LTN)
• Structural Logic Tensor Networks (sLTN)
• neurosymbolic framework
• first-order logic
• tensor operations
• differentiable learning
• structural organization
• temporal order
• sequential position
• graph connectivity

Claims Made by the Document

• sLTN is an extension of LTN.
• sLTN can handle structural organization.

Evidence Used

• The paper discusses sLTN as an extension of LTN.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.