We propose ILP-CoT, a method that bridges Inductive Logic Programming (ILP) and Multimodal Large Language Models (MLLMs) for abductive logical rule induction. The task involves both discovering logical facts and inducing logical rules from a small number of unstructured textual or visual inputs, which still remain challenging when solely relying on ILP, due to the requirement of specified background knowledge and high computational cost, or MLLMs, due to the appearance of perceptual hallucinations. Based on the key observation that MLLMs could propose structure-correct rules even under hallucinations, our approach automatically builds ILP tasks with pruned search spaces based on the rule structure proposals from MLLMs, and utilizes ILP system to output rules built upon rectified logical facts and formal inductive reasoning. Its effectiveness is verified through challenging logical induction benchmarks, as well as a potential application of our approach, namely text-to-image customized generation with rule induction. Our code and data are released at https://github.com/future-item/ILP-CoT.

Large language models (LLMs) achieve impressive results on advanced mathematics benchmarks but sometimes fail on basic arithmetic tasks, raising the question of whether they have truly grasped fundamental arithmetic rules or are merely relying on pattern matching. To unravel this issue, we systematically probe LLMs' understanding of two-integer addition ($0$ to $2^{64}$) by testing three crucial properties: commutativity ($A+B=B+A$), representation invariance via symbolic remapping (e.g., $7 \mapsto Y$), and consistent accuracy scaling with operand length. Our evaluation of 12 leading LLMs reveals a stark disconnect: while models achieve high numeric accuracy (73.8-99.8%), they systematically fail these diagnostics. Specifically, accuracy plummets to $\le 7.5$% with symbolic inputs, commutativity is violated in up to 20% of cases, and accuracy scaling is non-monotonic. Interventions further expose this pattern-matching reliance: explicitly providing rules degrades performance by 29.49%, while prompting for explanations before answering merely maintains baseline accuracy. These findings demonstrate that current LLMs address elementary addition via pattern matching, not robust rule induction, motivating new diagnostic benchmarks and innovations in model architecture and training to cultivate genuine mathematical reasoning. Our dataset and generating code are available at https://github.com/kuri-leo/llm-arithmetic-diagnostic.

Inductive reasoning enables humans to infer abstract rules from limited examples and apply them to novel situations. In this work, we compare an LLM-based hypothesis search framework with direct program generation approaches on few-shot rule induction tasks. Our findings show that hypothesis search achieves performance comparable to humans, while direct program generation falls notably behind. An error analysis reveals key bottlenecks in hypothesis generation and suggests directions for advancing program induction methods. Overall, this paper underscores the potential of LLM-based hypothesis search for modeling inductive reasoning and the challenges in building more efficient systems.

Legal rules encompass not only codified statutes but also implicit adjudicatory principles derived from precedents that contain discretionary norms, social morality, and policy. While computational legal research has advanced in applying established rules to cases, inducing legal rules from judicial decisions remains understudied, constrained by limitations in model inference efficacy and symbolic reasoning capability. The advent of Large Language Models (LLMs) offers unprecedented opportunities for automating the extraction of such latent principles, yet progress is stymied by the absence of formal task definitions, benchmark datasets, and methodologies. To address this gap, we formalize Legal Rule Induction (LRI) as the task of deriving concise, generalizable doctrinal rules from sets of analogous precedents, distilling their shared preconditions, normative behaviors, and legal consequences. We introduce the first LRI benchmark, comprising 5,121 case sets (38,088 Chinese cases in total) for model tuning and 216 expert-annotated gold test sets. Experimental results reveal that: 1) State-of-the-art LLMs struggle with over-generalization and hallucination; 2) Training on our dataset markedly enhances LLMs capabilities in capturing nuanced rule patterns across similar cases.

Rule-based models offer a human-understandable representation, i.e. they are interpretable. For this reason, they are used to explain the decisions of non-interpretable complex models, referred to as black box models. The generation of such explanations involves the approximation of a black box model by a rule-based model. To date, however, it has not been investigated whether the rule-based model makes decisions in the same way as the black box model it approximates. Decision making in the same way is understood in this work as the consistency of decisions and the consistency of the most important attributes used for decision making. This study proposes a novel approach ensuring that the rule-based surrogate model mimics the performance of the black box model. The proposed solution performs an explanation fusion involving rule generation and taking into account the feature importance determined by the selected XAI methods for the black box model being explained. The result of the method can be both global and local rule-based explanations. The quality of the proposed solution was verified by extensive analysis on 30 tabular benchmark datasets representing classification problems. Evaluation included comparison with the reference method and an illustrative case study. In addition, the paper discusses the possible pathways for the application of the rule-based approach in XAI and how rule-based explanations, including the proposed method, meet the user perspective and requirements for both content and presentation. The software created and a detailed report containing the full experimental results are available on the GitHub repository (https://github.com/ruleminer/FI-rules4XAI ).

We describe a neural network, called RufeNet, that learns explicit, sym(cid:173) bolic condition-action rules in a formal string manipulation domain. RuleNet discovers functional categories over elements of the domain, and, at various points during learning, extracts rules that operate on these categories. The rules are then injected back into RuleNet and training continues, in a process called iterative projection. By incorpo(cid:173) rating rules in this way, RuleNet exhibits enhanced learning and gener(cid:173) alization performance over alternative neural net approaches. By integrating symbolic rule learning and subsymbolic category learning, RuleNet has capabilities that go beyond a purely symbolic system.

Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence. However, in this era of big data, rule induction on the whole datasets is computationally intensive. So far, to the best of our knowledge, no known method focusing on accelerating rule induction has been reported. This is first study to consider the acceleration technique to reduce the scale of computation in rule induction. We propose an accelerator for rule induction based on fuzzy rough theory; the accelerator can avoid redundant computation and accelerate the building of a rule classifier. First, a rule induction method based on consistence degree, called Consistence-based Value Reduction (CVR), is proposed and used as basis to accelerate. Second, we introduce a compacted search space termed Key Set, which only contains the key instances required to update the induced rule, to conduct value reduction. The monotonicity of Key Set ensures the feasibility of our accelerator. Third, a rule-induction accelerator is designed based on Key Set, and it is theoretically guaranteed to display the same results as the unaccelerated version. Specifically, the rank preservation property of Key Set ensures consistency between the rule induction achieved by the accelerator and the unaccelerated method. Finally, extensive experiments demonstrate that the proposed accelerator can perform remarkably faster than the unaccelerated rule-based classifier methods, especially on datasets with numerous instances.

This article describes an action rule induction algorithm based on a sequential covering approach. Two variants of the algorithm are presented. The algorithm allows the action rule induction from a source and a target decision class point of view. The application of rule quality measures enables the induction of action rules that meet various quality criteria. The article also presents a method for recommendation induction. The recommendations indicate the actions to be taken to move a given test example, representing the source class, to the target one. The recommendation method is based on a set of induced action rules. The experimental part of the article presents the results of the algorithm operation on sixteen data sets. As a result of the conducted research the Ac-Rules package was made available.