Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical reasoning and critical for practical LLM agents and decision-making systems. However, evaluating LLMs as effective rule-based executors and planners remains underexplored. In this paper, we introduce LogicGame, a novel benchmark designed to evaluate the comprehensive rule understanding, execution, and planning capabilities of LLMs. Unlike traditional benchmarks, LogicGame provides diverse games that contain a series of rules with an initial state, requiring models to comprehend and apply predefined regulations to solve problems. We create simulated scenarios in which models execute or plan operations to achieve specific outcomes. These game scenarios are specifically designed to distinguish logical reasoning from mere knowledge by relying exclusively on predefined rules. This separation allows for a pure assessment of rule-based reasoning capabilities. The evaluation considers not only final outcomes but also intermediate steps, providing a comprehensive assessment of model performance. Moreover, these intermediate steps are deterministic and can be automatically verified. LogicGame defines game scenarios with varying difficulty levels, from simple rule applications to complex reasoning chains, in order to offer a precise evaluation of model performance on rule understanding and multi-step execution. Utilizing LogicGame, we test various LLMs and identify notable shortcomings in their rule-based logical reasoning abilities.

The high performance of tree ensemble classifiers benefits from a large set of rules, which, in turn, makes the models hard to understand. To improve interpretability, existing methods extract a subset of rules for approximation using model reduction techniques. However, by focusing on the reduced rule set, these methods often lose fidelity and ignore anomalous rules that, despite their infrequency, play crucial roles in real-world applications. This paper introduces a scalable visual analysis method to explain tree ensemble classifiers that contain tens of thousands of rules. The key idea is to address the issue of losing fidelity by adaptively organizing the rules as a hierarchy rather than reducing them. To ensure the inclusion of anomalous rules, we develop an anomaly-biased model reduction method to prioritize these rules at each hierarchical level. Synergized with this hierarchical organization of rules, we develop a matrix-based hierarchical visualization to support exploration at different levels of detail. Our quantitative experiments and case studies demonstrate how our method fosters a deeper understanding of both common and anomalous rules, thereby enhancing interpretability without sacrificing comprehensiveness.

Machine learning models are often criticized for their black-box nature, raising concerns about their applicability in critical decision-making scenarios. Consequently, there is a growing demand for interpretable models in such contexts. In this study, we introduce Model-based Deep Rule Forests (mobDRF), an interpretable representation learning algorithm designed to extract transparent models from data. By leveraging IF-THEN rules with multi-level logic expressions, mobDRF enhances the interpretability of existing models without compromising accuracy. We apply mobDRF to identify key risk factors for cognitive decline in an elderly population, demonstrating its effectiveness in subgroup analysis and local model optimization. Our method offers a promising solution for developing trustworthy and interpretable machine learning models, particularly valuable in fields like healthcare, where understanding differential effects across patient subgroups can lead to more personalized and effective treatments.

In process mining, a log exploration step allows making sense of the event traces; e.g., identifying event patterns and illogical traces, and gaining insight into their variability. To support expressive log exploration, the event log can be converted into a Knowledge Graph (KG), which can then be queried using general-purpose languages. We explore the creation of semantic KG using the Resource Description Framework (RDF) as a data model, combined with the general-purpose Notation3 (N3) rule language for querying. We show how typical trace querying constraints, inspired by the state of the art, can be implemented in N3. We convert case- and object-centric event logs into a trace-based semantic KG; OCEL2 logs are hereby "flattened" into traces based on object paths through the KG. This solution offers (a) expressivity, as queries can instantiate constraints in multiple ways and arbitrarily constrain attributes and relations (e.g., actors, resources); (b) flexibility, as OCEL2 event logs can be serialized as traces in arbitrary ways based on the KG; and (c) extensibility, as others can extend our library by leveraging the same implementation patterns.

Rule-based neural networks stand out for enabling interpretable classification by learning logical rules for both prediction and interpretation. However, existing models often lack flexibility due to the fixed model structure. Addressing this, we introduce the Normal Form Rule Learner (NFRL) algorithm, leveraging a selective discrete neural network, that treat weight parameters as hard selectors, to learn rules in both Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF) for enhanced accuracy and interpretability. Instead of adopting a deep, complex structure, the NFRL incorporates two specialized Normal Form Layers (NFLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Normal Form Constraint (NFC) to streamline neuron connections. We also show the novel network architecture can be optimized using adaptive gradient update together with Straight-Through Estimator to overcome the gradient vanishing challenge. Through extensive experiments on 11 datasets, NFRL demonstrates superior classification performance, quality of learned rules, efficiency and interpretability compared to 12 state-of-the-art alternatives. Code and data are available at \url{https://anonymous.4open.science/r/NFRL-27B4/}.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

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 .

As machine learning (ML) models and datasets increase in complexity, the demand for methods that enhance explainability and interpretability becomes paramount. Prototypes, by encapsulating essential characteristics within data, offer insights that enable tactical decision-making and enhance transparency. Traditional prototype methods often rely on sub-symbolic raw data and opaque latent spaces, reducing explainability and increasing the risk of misinterpretations. This paper presents a novel framework that utilizes semantic descriptions to define prototypes and provide clear explanations, effectively addressing the shortcomings of conventional methods. Our approach leverages concept-based descriptions to cluster data on the semantic level, ensuring that prototypes not only represent underlying properties intuitively but are also straightforward to interpret. Our method simplifies the interpretative process and effectively bridges the gap between complex data structures and human cognitive processes, thereby enhancing transparency and fostering trust. Our approach outperforms existing widely-used prototype methods in facilitating human understanding and informativeness, as validated through a user survey.

Venous thromboembolism (VTE) is a critical cardiovascular condition, encompassing deep vein thrombosis (DVT) and pulmonary embolism (PE). Accurate and timely identification of VTE is essential for effective medical care. This study builds upon our previous work, which addressed VTE detection using deep learning methods for DVT and a hybrid approach combining deep learning and rule-based classification for PE. Our earlier approaches, while effective, had two major limitations: they were complex and required expert involvement for feature engineering of the rule set. To overcome these challenges, we utilize the Mamba architecture-based classifier. This model achieves remarkable results, with a 97\% accuracy and F1 score on the DVT dataset and a 98\% accuracy and F1 score on the PE dataset. In contrast to the previous hybrid method on PE identification, the Mamba classifier eliminates the need for hand-engineered rules, significantly reducing model complexity while maintaining comparable performance. Additionally, we evaluated a lightweight Large Language Model (LLM), Phi-3 Mini, in detecting VTE. While this model delivers competitive results, outperforming the baseline BERT models, it proves to be computationally intensive due to its larger parameter set. Our evaluation shows that the Mamba-based model demonstrates superior performance and efficiency in VTE identification, offering an effective solution to the limitations of previous approaches.

Graph neural networks (GNNs) are frequently used to predict missing facts in knowledge graphs (KGs). Motivated by the lack of explainability for the outputs of these models, recent work has aimed to explain their predictions using Datalog, a widely used logic-based formalism. However, such work has been restricted to certain subclasses of GNNs. In this paper, we consider one of the most popular GNN architectures for KGs, R-GCN, and we provide two methods to extract rules that explain its predictions and are sound, in the sense that each fact derived by the rules is also predicted by the GNN, for any input dataset. Furthermore, we provide a method that can verify that certain classes of Datalog rules are not sound for the R-GCN. In our experiments, we train R-GCNs on KG completion benchmarks, and we are able to verify that no Datalog rule is sound for these models, even though the models often obtain high to near-perfect accuracy. This raises some concerns about the ability of R-GCN models to generalise and about the explainability of their predictions. We further provide two variations to the training paradigm of R-GCN that encourage it to learn sound rules and find a trade-off between model accuracy and the number of learned sound rules.