Building on existing work with Hyperblocks, which classify data using minimum and maximum bounds for each attribute, we focus on enhancing interpretability, decreasing training time, and reducing model complexity without sacrificing accuracy. This system allows subject matter experts (SMEs) to directly inspect and understand the model's decision logic without requiring extensive machine learning expertise. To reduce Hyperblock complexity while retaining performance, we introduce a suite of algorithms for Hyperblock simplification. These include removing redundant attributes, removing redundant blocks through overlap analysis, and creating disjunctive units. These methods eliminate unnecessary parameters, dramatically reducing model size without harming classification power. We increase robustness by introducing an interpretable fallback mechanism using k-Nearest Neighbor (k-NN) classifiers for points not covered by any block, ensuring complete data coverage while preserving model transparency. Our results demonstrate that interpretable models can scale to high-dimensional, large-volume datasets while maintaining competitive accuracy. On benchmark datasets such as WBC (9-D), we achieve strong predictive performance with significantly reduced complexity. On MNIST (784-D), our method continues to improve through tuning and simplification, showing promise as a transparent alternative to black-box models in domains where trust, clarity, and control are crucial.

This work uses visual knowledge discovery in parallel coordinates to advance methods of interpretable machine learning. The graphic data representation in parallel coordinates made the concepts of hypercubes and hyperblocks (HBs) simple to understand for end users. It is suggested to use mixed and pure hyperblocks in the proposed data classifier algorithm Hyper. It is shown that Hyper models generalize decision trees. The algorithm is presented in several settings and options to discover interactively or automatically overlapping or non-overlapping hyperblocks. Additionally, the use of hyperblocks in conjunction with language descriptions of visual patterns is demonstrated. The benchmark data from the UCI ML repository were used to evaluate the Hyper algorithm. It enabled the discovery of mixed and pure HBs evaluated using 10-fold cross validation. Connections among hyperblocks, dimension reduction and visualization have been established. The capability of end users to find and observe hyperblocks, as well as the ability of side-by-side visualizations to make patterns evident, are among major advantages ofhyperblock technology and the Hyper algorithm. A new method to visualize incomplete n-D data with missing values is proposed, while the traditional parallel coordinates do not support it. The ability of HBs to better prevent both overgeneralization and overfitting of data over decision trees is demonstrated as another benefit of the hyperblocks. The features of VisCanvas 2.0 software tool that implements Hyper technology are presented.

Understanding black-box Machine Learning methods on multidimensional data is a key challenge in Machine Learning. While many powerful Machine Learning methods already exist, these methods are often unexplainable or perform poorly on complex data. This paper proposes visual knowledge discovery approaches based on several forms of lossless General Line Coordinates. These are an expansion of the previously introduced General Line Coordinates Linear and Dynamic Scaffolding Coordinates to produce, explain, and visualize non-linear classifiers with explanation rules. To ensure these non-linear models and rules are accurate, General Line Coordinates Linear also developed new interactive visual knowledge discovery algorithms for finding worst-case validation splits. These expansions are General Line Coordinates non-linear, interactive rules linear, hyperblock rules linear, and worst-case linear. Experiments across multiple benchmark datasets show that this visual knowledge discovery method can compete with other visual and computational Machine Learning algorithms while improving both interpretability and accuracy in linear and non-linear classifications. Major benefits from these expansions consist of the ability to build accurate and highly interpretable models and rules from hyperblocks, the ability to analyze interpretability weaknesses in a model, and the input of expert knowledge through interactive and human-guided visual knowledge discovery methods.

Current Answer Set Programming (ASP) solvers largely build on Datalog, which, unlike general logic programming, lacks function symbols. This limitation makes ASP decidable, but greatly complicates the modeling of indefinite time, recursive data structures (e.g., lists), and infinite processes and objects in general. Recent research thus aims at finding decidable fragments of ASP with function symbols and studying their complexity. We identify bidirectional ASP programs as an expressive, but yet decidable, language that is useful, e.g., for reasoning about actions involving both the future and the past. We tightly characterize the computational complexity of bidirectional programs and some of their subclasses, addressing the main reasoning tasks. Our results also show that the recently introduced FDNC programs can be extended by inverse rules while retaining decidability, but computational costs are unavoidably higher.