The stakes of this conceptual muddle are not academic. Artificial intelligence is increasingly deployed in critical domains such as law and medicine, where decisions about bail, sentencing, diagnosis, and treatment can reshape human lives. The European Union’s AI Act, the world’s first comprehensive legal framework for artificial intelligence, explicitly demands transparency and explainability for high-risk systems. Yet the new paper observes that when lawmakers and technologists invoke explainability, they often talk past one another because they are not explaining the same thing. A lawyer asking why an algorithm flagged a defendant as high-risk is asking a different question from an engineer asking how the model’s weights were trained, and different again from an ethicist asking whether the system’s development process respected human rights. Without a shared vocabulary that distinguishes these questions, compliance analysis risks becoming a box-ticking exercise rather than genuine accountability.

The framework at the heart of the study decomposes explainability along two perpendicular axes, which the authors call horizontal and vertical levels. The horizontal axis addresses what can be explained in a system. The authors distinguish three such levels: first, the problem itself, meaning the task the AI system is intended to solve and the context in which it operates; second, the development of the system, encompassing the choices made in building it; and third, the system itself, the deployed artifact. This decomposition is deliberately fine-grained. The development level is further split between a static perspective, which considers the system’s design and documentation at a fixed point in time, and a dynamic perspective, which follows the evolution of the system across its lifecycle, including retraining and updating. The system level, in turn, is divided into explaining the input the system receives, the operations it performs, and the output it produces.

The vertical axis addresses the levels at which explanation can occur, and here the authors apply two criteria: the level of abstraction and the degree of formalisation of knowledge. An explanation pitched at a high level of abstraction might tell a hospital administrator that a diagnostic model “weighs imaging features alongside patient history,” while a low-abstraction explanation might enumerate the exact activation patterns inside a neural network. Similarly, knowledge can be formalised with mathematical precision or conveyed informally in natural language. The point, the authors argue, is that neither extreme is inherently better. The adequacy of an explanation depends on the audience, the purpose, and the regulatory context. A single AI system therefore admits a lattice of possible explanations, and conflating them produces exactly the kind of confusion that has plagued both public debate and legal compliance.

To demonstrate that the framework is more than an abstract taxonomy, the authors test it against three use cases drawn from contemporary controversy. The first maps Article 13 of the AI Act, which imposes transparency obligations on providers of high-risk AI systems. When the obligations in that article are parsed through the framework, it becomes clear that different clauses target different horizontal levels: some provisions demand explanation of the system’s operations, others of its development process, and still others of the problem definition and intended use. This mapping reveals both the strengths and the gaps of the legislation, showing regulators precisely where their demands sit on the conceptual grid and where important explanatory duties remain unaddressed.

The second use case revisits one of the most infamous episodes in the history of algorithmic justice: the debate surrounding COMPAS, the recidivism-prediction software whose alleged racial bias sparked years of dispute after a 2016 investigation. The authors show that much of the controversy can be reframed as a clash between explanations offered at different levels. One side analysed the system’s outputs statistically, asking whether error rates differed across racial groups; the other examined the system’s operations and inputs, asking whether race was used directly in the model. Because the combatants were explaining different things, the debate could not converge, and the framework makes visible exactly where the fault lines ran. The lesson is that clarifying the level of explanation upfront could defuse similar controversies before they harden into entrenched positions.

The third use case turns to the technology of the moment: large language model based AI chatbots such as conversational assistants. LLM systems are often described as especially opaque, but the framework allows a more precise diagnosis. The authors analyse opacity at each horizontal level, showing that while the low-level operations of a trained transformer network are effectively inaccessible to human inspection, explanations of the system’s inputs and outputs remain feasible, and explanations of the development process and the problem the system is meant to solve are available in principle. This stratified view suggests that declaring LLMs “black boxes” writ large is unhelpful; instead, developers and regulators can target specific levels where explanation is achievable, and be honest about levels where it is not.

Underlying the framework is a broader philosophical claim with technical consequences: AI systems are not unidimensional artifacts. A modern machine learning system comprises a problem formulation, a training pipeline, a data corpus, a model architecture, an inference mechanism, and an interface to users. Each of these components can be explained, but each demands different explanatory resources. Explaining the input might involve data provenance analysis and bias audits. Explaining operations might require interpretability techniques such as saliency maps, feature attribution, or mechanistic analysis. Explaining outputs might involve confidence calibration and counterfactual reasoning. Explaining development might mean documenting design decisions, hyperparameter choices, and evaluation protocols. The framework does not prescribe a single technique; it prescribes order. First decide what is being explained, then choose the method appropriate to that target.

The authors position their contribution explicitly as a theoretical and conceptual study, and they are careful about what it does and does not deliver. It does not provide new algorithms for generating explanations, nor does it offer empirical measurements of explanation quality. What it provides is conceptual clarity, a precondition for effective compliance analysis. In an era when organizations must certify the trustworthiness of AI systems against legal and ethical standards, a checklist that says “provide explanations” is vacuous unless it specifies which levels of explanation are required and at what abstraction and formalisation they should be pitched. The framework gives auditors, developers, and regulators a shared grid on which to locate every transparency requirement, making gaps and overlaps visible and enabling more systematic verification.

The research was conducted within a project funded by the European Union’s Horizon Europe Research and Innovation Programme under Grant Agreement number 101120406, with additional support from the DigiWorld Priority Research Area under the Strategic Programme Excellence Initiative at Jagiellonian University, and support for Andrzej Porębski from the Foundation for Polish Science. The work received on 2 May 2025 was accepted on 15 June 2026 and published on 7 September 2026, appearing as an open-access article that carries a permanent digital object identifier. The authors report no conflicts of interest relevant to the content of the study, and the article reflects only the authors’ views, with the European Commission bearing no responsibility for any use that may be made of the information it contains.

As artificial intelligence systems grow more capable and more embedded in consequential decisions, the pressure to make them accountable will only intensify. This study suggests that the path forward runs not through a single magic technique that will suddenly render neural networks transparent, but through disciplined thinking about the many different things we might mean when we ask a machine to explain itself. By separating the problem from the development process from the deployed system, and by distinguishing abstraction from formalisation in the explanations themselves, the Kraków team has offered regulators, engineers, and scholars a common map of the explanatory terrain. Whether that map becomes a standard tool of AI compliance will depend on uptake, but its central message is already clear: before demanding explanations from AI, we must first agree on what, exactly, we are asking to know.