sLTN: Structural Logic Tensor Networks

• URL: http://arxiv.org/abs/2608.11136v1
• Date: Tue, 11 Aug 2026 16:58:38 GMT
• Title: sLTN: Structural Logic Tensor Networks
• Abstract summary: We introduce sLTN, an extension of Logic Networks (LTN) that makes structural dimensions first-class elements of the language.<n>In the absence of structural dimensions, the framework recovers the original LTN semantics as a special case.<n>This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.
• Score: 5.9901156966011975
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Does Syntax Matter? A Graph-Augmented Variational Topic Model for Computational Social Sciences [51.56484100374058]
  This paper introduces the Structural Contextual Probabilistic Topic Model ( SCPTM), an architecture that incorporates syntactic dependency relations into topic inference.<n>We evaluate seven topic modeling techniques across four corpora differing in register and discourse structure.<n>Results show that SCPTM's neural architecture yields substantial gains in document-topic alignment over generative baselines.
  arXiv  Detail & Related papers  (2026-09-07T17:39:06Z)
• First-Order Temporal Logic Tensor Networks [47.56930079312276]
  We present First-Order Temporal Logic Networks (FOT-LTN) that is an extension of Logic Networks (LTN)<n>In particular, FOT-LTN joins the syntax of First-Order Linear Temporal Logic with the fuzzy (and real-valued) semantics of LTN.<n>A first evaluation regards a temporal knowledge graph completion task on two synthetic datasets with respect to dedicated (purely neural) methods.
  arXiv  Detail & Related papers  (2026-06-29T08:48:23Z)
• Weave of Formal Thought [51.56484100374058]
  We introduce Weave of Formal Thought (WoFT), a paradigm uniting rigorous syntactic validation with learned structural representations.<n>We present a latent-variable fine-tuning method training the language model to interleave non-terminal grammar symbols directly into generation.<n>For Python, fine-tuning StarCoder2-3B with our RWS objective reduces per-token cross-entropy by 14.3% relative to a text-only SFT baseline.
  arXiv  Detail & Related papers  (2026-06-24T15:58:11Z)
• SemStruct: Contextualizing Semantic Embeddings with Structural Information for Schema Matching [20.959946127503354]
  We propose SemStruct, a framework that joins the semantic power of frozen PLMs with the structural inductive bias of Graph Neural Networks (GNNs)<n>We model the table as a heterogeneous graph where columns and values are nodes connected by rows, allowing the GNN to propagate disambiguating context across the structure.
  arXiv  Detail & Related papers  (2026-05-29T01:45:45Z)
• Unifying approach to uniform expressivity of graph neural networks [4.640835690336653]
  Graph Neural Networks (GNNs) are often analysed via correspondence to the Weisfeiler-Leman (WL) algorithm and fragments of first-order logic.<n>Standard GNNs are limited to performing aggregation over immediate neighbourhoods or over global read-outs.<n>To increase their expressivity, recent attempts have been made to incorporate substructural information (e.g. cycle counts and subgraph properties)
  arXiv  Detail & Related papers  (2026-02-20T18:18:48Z)
• LSRIF: Logic-Structured Reinforcement Learning for Instruction Following [56.517329105764475]
  We propose a logic-structured training framework LSRIF that explicitly models instruction logic.<n> Experiments show LSRIF brings significant improvements in instruction-following and general reasoning.
  arXiv  Detail & Related papers  (2026-01-10T05:11:38Z)
• Semantic Loss Functions for Neuro-Symbolic Structured Prediction [74.18322585177832]
  We discuss the semantic loss, which injects knowledge about such structure, defined symbolically, into training. It is agnostic to the arrangement of the symbols, and depends only on the semantics expressed thereby. It can be combined with both discriminative and generative neural models.
  arXiv  Detail & Related papers  (2024-05-12T22:18:25Z)
• PROTOtypical Logic Tensor Networks (PROTO-LTN) for Zero Shot Learning [2.236663830879273]
  Logic Networks (LTNs) are neuro-symbolic systems based on a differentiable, first-order logic grounded into a deep neural network. We focus here on the subsumption or textttisOfClass predicate, which is fundamental to encode most semantic image interpretation tasks. We propose a common textttisOfClass predicate, whose level of truth is a function of the distance between an object embedding and the corresponding class prototype.
  arXiv  Detail & Related papers  (2022-06-26T18:34:07Z)
• Modeling Hierarchical Structures with Continuous Recursive Neural Networks [33.74585832995141]
  Recursive Neural Networks (RvNNs) compose sequences according to their underlying hierarchical syntactic structure. Traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. We propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative.
  arXiv  Detail & Related papers  (2021-06-10T20:42:05Z)
• NSL: Hybrid Interpretable Learning From Noisy Raw Data [66.15862011405882]
  This paper introduces a hybrid neural-symbolic learning framework, called NSL, that learns interpretable rules from labelled unstructured data. NSL combines pre-trained neural networks for feature extraction with FastLAS, a state-of-the-art ILP system for rule learning under the answer set semantics. We demonstrate that NSL is able to learn robust rules from MNIST data and achieve comparable or superior accuracy when compared to neural network and random forest baselines.
  arXiv  Detail & Related papers  (2020-12-09T13:02:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.