The subject of the research is the development of mathematical and algorithmic support of the intellectual toolkit for the analysis of sets of test tasks and the modeling of the process of interpreting the quality of sets of test tasks, which allows for objective and comprehensive continuous control of the knowledge of subjects of training, subject to the implementation of the concept of virtual distributed training (retraining).
 The purpose of the research is to improve the effectiveness of monitoring the knowledge of subjects of education in the distance form of education through the use of adaptive computer testing methods based on models of logical networks and the algebra of finite predicates.
 The following tasks are solved in the article: the formation of a testing model in a distributed virtual learning environment and a model of validity assessment based on the content of sets of test tasks.
 The following methods are used: methods of logical networks and algebraic programming based on the algebra of finite predicates and predicate operations, intellectual analysis of information.
 The following results were obtained: the principles of intellectual analysis were formulated in the development of a model of a universal logical network and its application to actual tasks of artificial intelligence in the field of informal information processing, namely, in the construction of knowledge testing systems for distributed virtual learning
 Conclusions. Algorithms for optimal multi-stage adaptive testing of knowledge as part of distributed virtual learning models and methods for analyzing the success of training subjects have been improved. The use of conjunctive decomposition with binary predicates achieves the goal of the research, because in this way any multi-place predicate can be represented by a logical network simulating the process of knowledge testing, the model of the subject of learning is described.
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