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The paper presents discretion in applying provisions of law as an assessment when making a decision or as the choice of the most appropriate and fair decision from among the options allowed by law. This legal phenomenon has been represented as an oriented causal graph, in which all events are related to each other, are each other’s causes or consequences. Each of its points-vertices is an event, the edge is a connection, the orientation of the edges is from consequence to cause. Peculiarities of the European legislation on AI have been dealt with. The essence of a discretionary decision-making AI module has been researched into. The emphasis has been made on the AI and machine learning model which could be: functional, dynamic, embodied in terms of mathematical functions, models of risks, optimization of lending; static, embodied in the relationships between data objects (chart of accounts, relationships between subjects). The Abstraction and Reasoning Corpus data array has been demonstrated as a reference test of strong AI. The methods of controlled machine learning have been revealed, covering organized learning (‘student task’), inductive programming (‘life experience’), predictive power (‘scientist’s task’), organization of training (‘teacher’s task’). The classification of arguments, methodologies and approaches has been identified for the discretionary decision-making process with the relevant case of the European Court of Human Rights.