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Abstract Recentneuro-symbolic approaches have successfully extracted symbolic rule-sets from Convolutional Neural Network-based models to enhance interpretability. However, applying similar techniques to Vision Transformers (ViTs) remains challenging due to their lack of modular concept detectors and reliance on global self-attention mechanisms. We propose a framework for symbolic rule extraction from ViTs by introducing a sparse concept layer inspired by Sparse Autoencoders (SAEs). This linear layer operates on attention-weighted patch representations and learns a disentangled, binarized representation in which individual neurons activate for high-level visual concepts. To encourage interpretability, we apply a combination of L1 sparsity, entropy minimization, and supervised contrastive loss. These binarized concept activations are used as input to the FOLD-SE-M algorithm, which generates a rule-set in the form of a logic program. Our method achieves abetter classification accuracy than the standard ViT while enabling symbolic reasoning. Crucially, the extracted rule-set is not merely post-hoc but acts as a logic-based decision layer that operates directly on the sparse concept representations. The resulting programs are concise and semantically meaningful. This work is the first to extract executable logic programs from ViTs using sparse symbolic representations, providing a step forward in interpretable and verifiable neuro-symbolic AI. 

Abstract FOLD-RM is an automated inductive learning algorithm for learning default rules for mixed (numerical and categorical) data. It generates an (explainable) answer set programming (ASP) rule set for multi-category classification tasks while maintaining efficiency and scalability. The FOLD-RM algorithm is competitive in performance with the widely used, state-of-the-art algorithms such as XGBoost and multi-layer perceptrons, however, unlike these algorithms, the FOLD-RM algorithm produces an explainable model. FOLD-RM outperforms XGBoost on some datasets, particularly large ones. FOLD-RM also provides human-friendly explanations for predictions. 

FOLD-R is an automated inductive learning algorithm for learning default rules for mixed (numerical and categorical) data. It generates an (explainable) normal logic program (NLP) rule set for classification tasks. We present an improved FOLD-R algorithm, called FOLD-R++, that significantly increases the efficiency and scalability of FOLD-R by orders of magnitude. FOLD-R++ improves upon FOLD-R without compromising or losing information in the input training data during the encoding or feature selection phase. The FOLD-R++ algorithm is competitive in performance with the widely-used XGBoost algorithm, however, unlike XGBoost, the FOLD-R++ algorithm produces an explainable model. FOLD-R++ is also competitive in performance with the RIPPER system, however, on large datasets FOLD-R++ outperforms RIPPER. We also create a powerful tool-set by combining FOLD-R++ with s(CASP)—a goal-directed answer set programming (ASP) execution engine—to make predictions on new data samples using the normal logic program generated by FOLD-R++. The s(CASP) system also produces a justification for the prediction. Experiments presented in this paper show that our improved FOLD-R++ algorithm is a significant improvement over the original design and that the s(CASP) system can make predictions in an efficient manner as well. 

Abstract Multi-core and highly connected architectures have become ubiquitous, and this has brought renewed interest in language-based approaches to the exploitation of parallelism. Since its inception, logic programming has been recognized as a programming paradigm with great potential for automated exploitation of parallelism. The comprehensive survey of the first twenty years of research in parallel logic programming, published in 2001, has served since as a fundamental reference to researchers and developers. The contents are quite valid today, but at the same time the field has continued evolving at a fast pace in the years that have followed. Many of these achievements and ongoing research have been driven by the rapid pace of technological innovation, that has led to advances such as very large clusters, the wide diffusion of multi-core processors, the game-changing role of general-purpose graphic processing units, and the ubiquitous adoption of cloud computing. This has been paralleled by significant advances within logic programming, such as tabling, more powerful static analysis and verification, the rapid growth of Answer Set Programming, and in general, more mature implementations and systems. This survey provides a review of the research in parallel logic programming covering the period since 2001, thus providing a natural continuation of the previous survey. In order to keep the survey self-contained, it restricts its attention to parallelization of the major logic programming languages (Prolog, Datalog, Answer Set Programming) and with an emphasis on automated parallelization and preservation of the sequential observable semantics of such languages. The goal of the survey is to serve not only as a reference for researchers and developers of logic programming systems but also as engaging reading for anyone interested in logic and as a useful source for researchers in parallel systems outside logic programming. 

We focus on the problem of inducing logic programs that explain models learned by the support vector machine (SVM) algorithm. The top-down sequential covering inductive logic programming (ILP) algorithms (e.g., FOIL) apply hill-climbing search using heuristics from information theory. A major issue with this class of algorithms is getting stuck in local optima. In our new approach, however, the data-dependent hill-climbing search is replaced with a model-dependent search where a globally optimal SVM model is trained first, then the algorithm looks into support vectors as the most influential data points in the model, and induces a clause that would cover the support vector and points that are most similar to that support vector. Instead of defining a fixed hypothesis search space, our algorithm makes use of SHAP, an example-specific interpreter in explainable AI, to determine a relevant set of features. This approach yields an algorithm that captures the SVM model’s underlying logic and outperforms other ILP algorithms in terms of the number of induced clauses and classification evaluation metrics. 

Understanding the meaning of a text is a fundamental challenge of natural language understanding (NLU) research. An ideal NLU system should process a language in a way that is not exclusive to a single task or a dataset. Keeping this in mind, we have introduced a novel knowledge driven semantic representation approach for English text. By leveraging the VerbNet lexicon, we are able to map syntax tree of the text to its commonsense meaning represented using basic knowledge primitives. The general purpose knowledge represented from our approach can be used to build any reasoning based NLU system that can also provide justification. We applied this approach to construct two NLU applications that we present here: SQuARE (Semantic-based Question Answering and Reasoning Engine) and StaCACK (Stateful Conversational Agent using Commonsense Knowledge). Both these systems work by ``truly understanding'' the natural language text they process and both provide natural language explanations for their responses while maintaining high accuracy.