Artificial intelligence approaches, particularly neural network technology, play an increasingly important role in modern systems for detecting and preventing intrusions in computer systems and networks. Existing classification models reveal system’s anomalous behavior and the type of intrusion to which an attacked system is exposed. However, neural network technology has several problems, such as false positive detections, adversarial attacks, heterogeneity of training sets, and the inability to classify intrusions outside of the training dataset. The use of algebraic methods and modern solver systems for the accurate detection of real-time attacks is not common, as they are much slower than neural network classification. This work uses formal constructs, such as cognitive networks, to leverage the synergy between neural network technology and algebraic methods. These constructs are a composition of a neural network and transition system networks based on algebraic behavioral models. The use of algebraic modeling technologies and neural networks is demonstrated with examples that present the real-time prevention of attacks in software and network environments. This paper demonstrates the use of a cognitive network that combines these two techniques as a novel approach for model training and cyberattack detection.