sLTN: Structural Logic Tensor Networks

Logic Tensor Networks (LTN) are a neurosymbolic framework that bridges first-order logic and deep learning by interpreting logical formulas as differentiable tensor operations. While effective for flat data, standard LTN struggles to capture inherent structural dependencies like temporal order or graph topology. The authors introduce sLTN to address this by making structural dimensions—such as time steps or sequence indices—explicit components of the logical syntax and semantics.

sLTN extends the traditional LTN signature by adding structural dimensions and structural variables. These allow users to define logical constraints that operate over specific axes of a tensor. For instance, a temporal relation can be used to enforce that a property holds across consecutive time steps. The framework maintains the core LTN advantage: it uses fuzzy logic to map formulas to differentiable values, allowing the system to optimize logical satisfiability via gradient descent. The authors provide a modular PyTorch implementation that separates the declarative signature from the tensorial interpretation, ensuring that the system remains flexible for various structured data tasks.

By integrating structural awareness directly into the neurosymbolic loop, sLTN enables more expressive reasoning over complex data types like time series, video sequences, and graphs. This approach allows researchers to inject domain-specific structural knowledge—such as physical laws or sequential constraints—directly into neural models, potentially improving performance and interpretability in scenarios where data is sparse or requires strict adherence to relational rules.