(untitled) (Contemporary Mathematics, 2025)
The integration of domain and expert knowledge into AI systems represents a critical advancement, with profound implications for solving complex, multidisciplinary challenges. The formal representation of domain and expert knowledge in these systems, combined with AI techniques, has enabled the fusion of human expertise with technologies such as machine learning (ML) and natural language processing (NLP), significantly enhancing decision-making and predictive capabilities. This paper provides a systematic review of the mathematical and computational techniques employed to integrate domain and expert knowledge into artificial intelligence (AI) systems for the development of expert systems, evaluating a total of 907 studies. The results demonstrate substantial growth in the mathematical andalgorithmic foundations of expert systems since the 1980s, highlighting key trends in the integration of AI technologies. The challenges and benefits of these approaches across various domains are discussed, emphasizing their mathematical rigor and practical significance.