arXiv:2608. 16443v1 Announce Type: new Abstract: Neurosymbolic (NeSy) Artificial Intelligence aims to integrate Deep Learning (DL) architectures with symbolic reasoning.
The paper introduces recurrent Graph Neural Networks (GNNs) that use set-based aggregation and establishes conditions that can be verified directly from the network weights. It proves a two‑directional equivalence between these networks and the Boolean closure of reachability and safety properties, corresponding to the fragment BΣ◦₁ of the modal μ‑calculus. This equivalence allows for verifiable symbolic explanations of networks that satisfy the identified conditions, without relying on counting logic or external halting signals.
arXiv:2606. 29972v1 Announce Type: new Abstract: Most of the existing neuro-symbolic AI methods focus on the scenario of static knowledge where objects do not change according to a temporal dimension.
arXiv:2605. 30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches.
arXiv:2606. 19279v1 Announce Type: new Abstract: Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules.
arXiv:2608. 11136v1 Announce Type: new 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.
arXiv:2606. 17882v1 Announce Type: new Abstract: Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions.
The paper introduces the Native Predicate Neuron, a differentiable logic‑reasoning module that can be inserted into standard neural architectures. It learns to alternate between logical operations using a single trainable parameter and employs a dual‑nature gradient mechanism that performs hard logical operations during training while remaining differentiable for backpropagation. Experiments on Fully‑Connected, Convolutional, Recurrent, and Transformer models show that adding Predicate Neurons speeds convergence, improves accuracy, and reduces loss, especially on tasks involving monotonic reasoning or discontinuities.
NeuroRule is a knowledge distillation framework that transforms high‑capacity neural networks into explainable rule‑sets. It adapts the EVOTER rule‑set evolution infrastructure to evolve propositional logic expressions that capture the neural network’s performance. The approach includes a conciseness objective to enhance explainability and demonstrates viability even without access to the original training data.
arXiv:2607. 20402v1 Announce Type: new Abstract: In many reasoning problems, the premises are not observed as discrete symbols, but must be inferred from high-dimensional inputs.
arXiv:2608.21605v1 Announce Type: new Abstract: Logic Tensor Network-Enhanced Generative Adversarial Networks (LTN-GANs) inject background knowledge by grounding each logical axiom as a predicate and...
arXiv:2607. 24275v1 Announce Type: cross Abstract: Ethical governance of AI-driven systems is often expressed through high-level principles and static documentation, creating a gap between regulatory requirements and system-level verification.