Abstract
Kleene algebras (KA) and Kleene algebras with tests (KAT) provide an algebraic framework to capture the behavior of conventional programming constructs. This paper explores a broader understanding of these structures, in order to enable the expression of programs and tests yielding vague or inconsistent outcomes. Within this context, we introduce the concept of a paraconsistent Kleene Algebra with tests (PKAT), capable of capturing vague and contradictory computations. Finally, to establish the semantics of such a structure, we introduce two algebras, SetP(T) and RelP(K,T), parametric on a class of twisted structures K and T. We believe this sort of structures, for their huge flexibility, have an interesting application potential.

Abstract
The growing deployment of artificial intelligence in critical domains exposes a pressing challenge: how reliably models make predictions for ambiguous data without exhibiting overconfidence. We introduce hubris benchmarking, a methodology to evaluate overconfidence in machine learning models. The benchmark is based on a novel architecture, ambiguous generative adversarial networks (AmbiGANs), which are trained to synthesize realistic yet ambiguous datasets. We also propose the hubris metric to quantitatively measure the extent of model overconfidence when faced with these ambiguous images. We illustrate the usage of the methodology by estimating the hubris of state-of-the-art pre-trained models (ConvNext and ViT) on binarized versions of public datasets, including MNIST, Fashion-MNIST, and Pneumonia Chest X-ray. We found that, while ConvNext is on average 3% more accurate than ViT, it often makes excessively confident predictions, on average by 10% points higher than ViT. These results illustrate the usefulness of hubris benchmarking in high-stakes decision processes. © 2025 Elsevier B.V., All rights reserved.

Abstract
To get products delivered, clients and retailers agree on a delivery time window. We collaborated with an online retailer to develop a real-world application aimed at dynamically determining the delivery fee for each time window while ensuring the explainability of the pricing policy. This sequential decision-making problem arises as new customers continuously arrive. The objective is to maximize the final profit, given by the sum of baskets and delivery fees, discounted by the transportation and fleet costs. As multiple customers share the same delivery route, the costs are distributed among them, complicating the calculation of the marginal cost of each customer. Our study employs Genetic Programming (GP) to create explainable and easy-to-compute pricing policies to determine the delivery fees. These policies, expressed as mathematical formulas, rank price panels combinations of time slots and corresponding fees to identify optimal prices for each customer. The inputs to the GP algorithm capture the current state of the system, including factors such as capacity, customer location, and basket value. The resulting expressions offer operational managers a transparent pricing policy that allows them to maximize total profit.

Abstract
The increasing integration of renewable energy sources and decentralized generation requires demand-side flexibility to improve grid stability and balance local energy flows. Local Flexibility Markets (LFMs) provide a framework for optimizing flexibility transactions within energy communities. This paper presents a model for quantifying and pricing residential resources flexibility, enabling prosumers to submit bids in an LFM managed by the Community Manager. The methodology relies on a linear optimization problem, where a Home Energy Management System first determines optimal consumption baselines. Then an iterative sensitivity analysis estimates upward, and downward flexibility bands and sets offer prices per resource. The market operates as two asymmetric voluntary pools, clearing flexibility offers and requests. Results show that Battery Energy Storage Systems and Electric Vehicles provide the most effective flexibility, significantly reducing energy costs. Future research should improve pricing mechanisms and scalability to support LFM adoption in different residential settings.

Abstract
Secure Multiparty Computation (SMC) facilitates secure collaboration among multiple parties while safeguarding the privacy of their confidential data. This paper introduces a two-party quantum SMC protocol designed for evaluating binary Boolean functions using single qubits. Complexity analyses demonstrate a reduction of 66.7% in required quantum resources, achieved by utilizing single qubits instead of multi-particle entangled states. However, the quantum communication cost has increased by 40% due to the amplified exchange of qubits among participants. Furthermore, we bolster security by performing additional quantum operations along the y-axis of the Bloch sphere, effectively hiding the output from potential adversaries. We design the corresponding quantum circuit and implement the proposed protocol on the IBM Qiskit platform, yielding reliable outcomes.

Abstract
A subgroup discovery-based method has recently been proposed to understand the behavior of models in the (original) feature space. The subgroups identified represent areas of feature space where the model obtains better or worse predictive performance when compared to the average test performance. For instance, in the marketing domain, the approach extracts subgroups such as: in groups of customers with higher income and who are younger, the random forest achieves higher accuracy than on average. Here, we propose a complementary method, Meta Subspace Analysis (MSA), MSA uses metalearning to analyze these subgroups in the metafeature space. We use association rules to relate metafeatures of the feature space represented by the subgroups to the improvement or degradation of the performance of models. For instance, in the same domain, the approach extracts rules such as: when the class entropy decreases and the mutual information increases in the subgroup data, the random forest achieves lower accuracy. While the subgroups in the original feature space are useful for the end user and the data scientist developing the corresponding model, the meta-level rules provide a domain-independent perspective on the behavior of the model that is suitable for the same data scientist but also for ML researchers, to understand the behavior of algorithms. We illustrate the approach with the results of two well-known algorithms, naive Bayes and random forest, on the Adult dataset. The results confirm some expected behavior of algorithms. However, and most interestingly, some unexpected behaviors are also obtained, requiring additional investigation. In general, the empirical study demonstrates the usefulness of the approach to obtain additional knowledge about the behavior of models. © 2025 Elsevier B.V., All rights reserved.