Vol 15, No 1 (2025)

The article discusses the inconsistency of three "indisputable" principles in modern logic: the inconsistency of the concept of "set," the absolute necessity of axioms in logic, and the infallibility of syllogistic reasoning. To address the first misconception, the authors propose incorporating the algebra of sets into the foundations of logic, following the approach outlined in R. Courant and G. Robbins' book What is Mathematics? The second misconception is addressed by deriving known laws of algebra of sets, corresponding to classical logic, through the enumeration method. The third misconception is resolved by developing a mathematical model of polysyllogistic reasoning based on the laws of algebra of sets. The novelty of this proposed reasoning model lies in introducing restrictions alongside premises, with any violation of these restrictions signaling errors in reasoning. This model enhances the analytical capabilities of logical analysis, enabling the detection of errors in traditional syllogistic reasoning, including instances where some correct inferences are classified as "incorrect" modes. Furthermore, new laws of algebra of sets are formulated and justified: the law of paradox, the condition of non-empty intersection, and the law of existence.

The paper suggests distinguishing between the methodologies of conceptual analysis and notional analysis. The difference lies in how the notion and concept are interpreted. In the paper, a notion is viewed as an individual opinion or understanding of something, whereas a concept represents a general notion or abstract idea. It is assumed that many similar concepts exist with varying scopes and contents. A concept is treated as an objectified notion developed and solidified through social experience. The primary representation of the results of established conceptual analysis methods is shown to be a semantic network, where the vertices are concepts and the arcs represent relationships between them. However, it is noted that classical set theory and semantic networks are insufficient to formalize notions and concepts; instead, the theory of structures must be employed. Conceptual analysis is described as a technique for synthesizing formal concept descriptions using Boolean and Cartesian construction operations. The challenges of applying conceptual analysis within the framework of the theory of structures are outlined. The development of notional analysis is linked to the demand for precise, unambiguous, and consistent notion descriptions, driven by the variability of their properties. Notional analysis is defined as a method for formal normal descriptions using generalization and association operations. Generalization entails combining notions such that the entities of the generalized notions become entities of the resulting notion. Association involves merging notions, with each entity of the resulting notion including one entity from each of the associated notions. Notional analysis addresses issues encountered when describing concepts using a corpus-based approach by generating diverse descriptions of notions. It is demonstrated that both conceptual and notional analyses are rooted in the theory of structures. The paper identifies areas where these analyses are effectively applied and provides an example of using notional analysis in the design of a technical device.

The paper presents a method for building a knowledge graph from telecommunication data using proprietary and reference models commonly employed in the telecommunications domain. Reference models are based on those included in the framework developed by the TM Forum consortium. The proposed approach involves building a knowledge graph for proprietary models through automated processing of autotest log files and billing system database tables. The relevance of knowledge graphs stems from their structured and semantic nature, as well as their potential for applying machine learning algorithms to generate recommendations for optimizing telecommunication processes and systems. A method based on a multi-step reasoning approach is proposed for creating interpretable recommendations by predicting and restoring missing links in a proprietary knowledge graph. This approach treats multi-step reasoning as a question-answering task using natural language processing techniques. The implementation of the proposed solution, leveraging a transformer-based neural network architecture, yielded interpretable results while maintaining metric values comparable to existing methods.

In academic disciplines, students are required to learn many new concepts, which necessitates extensive training with feedback. An intelligent simulator enables students to practice solving simple problems while receiving explanations for their mistakes, allowing teachers to focus on addressing more complex issues during lessons. This paper presents a method for developing intelligent simulators based on the ontology of the subject domain, implemented as web applications suitable for both classroom and extracurricular use. Representing the problem and the subject area model in RDF format enables logical inference using the Apache Jena Reasoner inference engine. An example is provided of an intelligent simulator designed for learning the order of operations in expressions, supporting the C++, C#, and Python programming languages. The simulator can explain errors, generate explanatory hints, and engage in educational dialogue through guiding questions. The simulator was tested with undergraduate and graduate students of the Faculty of Electronics and Computer Engineering at Volgograd State Technical University. Most students found the simulator to be more useful than traditional training tests. It can be employed both for independent study and as part of the educational process in classroom settings.

In industrial Internet of Things (IoT) systems, explaining anomalies plays a crucial role in identifying bottlenecks and optimizing processes. This paper proposes an approach to anomaly detection using an autoencoder and its explanation based on the SHAP method. The purpose of the anomaly explanation is to provide a set of data features in industrial IoT systems that most significantly influence anomaly detection. The novelty of this approach lies in its ability to quantify the contribution of individual features for specific data samples and to calculate an average contribution across the dataset, providing a feature importance ranking. The proposed approach is tested on Industrial IoT datasets with varying feature counts and data volumes. The anomaly detection achieves an F-measure of 88-93%, outperforming the comparable methods discussed. The study demonstrates how explainable artificial intelligence can identify the causes of anomalies in both individual samples and datasets as a whole. The theoretical importance of the proposed approach lies in its ability to shed light on the workings of intelligent detection models, enabling the identification of factors influencing their outcomes and uncovering previously unnoticed patterns. In practice, this method enhances security system operators' understanding of ongoing processes, aiding in threat identification and error detection within data.

The findings presented in this paper rely on system archetypes, which serve as unified conceptual models for addressing organizational challenges in managing complex systems. These archetypes facilitate the creation of comparable descriptions of problem situations by accommodating differing perspectives of stakeholders (actors) on the factors hindering the integration of local systems. The research framework integrates system archetypes with the House of Quality model and employs correlation coefficients—rank, partial, and multiple. An example of multi-faceted modeling is provided, wherein the calculated correlation coefficients act as indicators of the degree of alignment in actors' views regarding the factors of the problem situation. Multiple correlation coefficients are interpreted as measures of the consistency of an individual actor’s opinions with those of the collective group, while partial correlation coefficients gauge the alignment of opinions between specific pairs of actors. The proposed methodology for quantitatively assessing the alignment of heterogeneous actors' perspectives enables the evaluation of the effectiveness of initiatives aimed at building a communication framework that supports the development of a shared understanding of the significance of various factors in a problem situation.