The article deals with research related to the use of artificial intelligence technologies for effective decision-making in corporate governance under conditions of deep uncertainty. To process uncertainty, it is proposed to use the cognitive capabilities of artificial intelligence. Cognitivism can be used to implement intuitive, psychological and other components of the internal mental activity of a person when making decisions. These capabilities allow one to make informed decisions and predict the consequences of these decisions. To study the properties of deep uncertainty, the authors suggest using a tensor model. The tensor model of deep uncertainty makes it possible to study additional properties of uncertainty that are not available in traditional models, such as Bayesian formalism, Dempster-Shafer theory, fuzzy sets, a method based on certain factors (Stanford formalism), and others. The use of the tensor model allows one to study the spatial model of uncertainty, real and imaginary values of uncertainty, as well as uncertainty invariants with respect to various transformations of the coordinate system.