The concept of conditional independence (CI) plays an essential role in the area of decision-making under uncertainty (in artificial intelligence), in particular, in the area of probabilistic reasoning. The aim of the project is to try to solve mathematical problems which arise in connection with the methods of computer representation of CI structures and their learning based on data. Procedures and knowledge from several areas of mathematics are utilized in this area: the methods of information theory are combined with algebraic methods, methods of discrete mathematics (graphs) and methods of mathematical statistics. The project has 3 main goals. The first goal is, following a general method of description of CI structures by means of integer-valued vectors developed within a previous project, to introduce a non-graphical arithmetic method of learning graphical models from data. The second goal is find out whether the methods of algebraic statistics, which is an emerging branch of