Multimodal symbolic logical reasoning, which aims to deduce new facts from multimodal input via formal logic, is critical in high-stakes applications such as autonomous driving and medical diagnosis, as its rigorous, deterministic reasoning helps prevent serious consequences. To evaluate such capabilities of current state-of-the-art vision language models (VLMs), we introduce MuSLR, the first multimodal symbolic logical reasoning grounded in formal logical rules. We curate a benchmark dataset for MuSLR comprising 1,093 instances across 7 domains, including 35 atomic symbolic logic and 976 logical combinations, with reasoning depths ranging from 2 to 9. We evaluate 7 state-of-the-art VLMs on our benchmark and find that they all struggle with multimodal symbolic reasoning, with the best model, GPT-4.1, achieving only 46.8%. Thus, we propose LogiCAM, a modular framework that applies formal logical rules to multimodal inputs, boosting GPT-4.1's

Inductive relation prediction (IRP)--where entities can be different during training and inference--has shown great power for completing evolving knowledge graphs. Existing works mainly focus on using graph neural networks (GNNs) to learn the representation of the subgraph induced from the target link, which can be seen as an implicit rule-mining process to measure the plausibility of the target link. However, these methods cannot differentiate the target link and other links during message passing, hence the final subgraph representation will contain irrelevant rule information to the target link, which reduces the reasoning performance and severely hinders the applications for real-world scenarios. To tackle this problem, we propose a novel single-source edge-wise GNN model to learn the Rule-inducEd Subgraph represenTations (REST), which encodes relevant rules and eliminates irrelevant rules within the subgraph. Specifically, we propose a single-source initialization approach to initialize edge features only for the target link, which guarantees the relevance of mined rules and target link. Then we propose several RNN-based functions for edge-wise message passing to model the sequential property of mined rules. REST is a simple and effective approach with theoretical support to learn the rule-induced subgraph representation. Moreover, REST does not need node labeling, which significantly accelerates the subgraph preprocessing time by up to 11.66 . Experiments on inductive relation prediction benchmarks demonstrate the effectiveness of our REST2.

We introduce deep neural networks for end-to-end differentiable theorem proving that operate on dense vector representations of symbols. These neural networks are recursively constructed by following the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. The resulting neural network can be trained to infer facts from a given incomplete knowledge base using gradient descent. By doing so, it learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove facts, (iii) induce logical rules, and (iv) it can use provided and induced logical rules for complex multi-hop reasoning. On four benchmark knowledge bases we demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, while at the same time inducing interpretable function-free first-order logic rules.

In this paper, we propose a two-stage framework that imposes both structural and textual knowledge to learn rule-based systems. In the first stage, we compute a set of triples with confidence scores (called soft triples) from a text corpus by distant supervision, where a textual entailment model with multi-instance learning is exploited to estimate whether a given triple is entailed by a set of sentences. In the second stage, these soft triples are used to learn a rule-based model for KGC.

Neural Information Processing Systems http://nips.cc/

Bridging logical reasoning and deep learning is crucial for advanced AI systems.

Figure 1 illustrates model predictions across every Number Game concept in [33].Figure 6: Model predictions across every Number Game concept in [33] (Figure 1). For the number game, every model has its outputs transformed by a learned Platt transform. Logical concept models do not use Platt transforms. We fit these parameters using Adam with a learning rate of 0.001. For the number game we do 10-fold cross validation to calculate holdout predictions.