Published Paper Details:

Knowledge Representation and Reasoning (KR&R) forms the backbone of intelligent systems, enabling machines to encode, manipulate, and infer knowledge about the world. This paper presents a comprehensive review and technical analysis of the core concepts, methodologies, and mathematical foundations of KR&R, with a focus on their application in modern intelligent systems. We systematically examine classical logic-based approaches, ontologies, semantic models, rule-based systems, and frameworks for reasoning under uncertainty, including probabilistic and fuzzy logic. The paper details formal mathematical notations for logic and reasoning, and provides comparative analyses of major KR techniques. Recent advancements such as knowledge graphs, ontological reasoning, and explainable AI are discussed, highlighting their transformative impact on AI applications. Real-world use cases in expert systems, natural language processing, robotics, and the semantic web are explored. The paper also addresses current challenges, research gaps, and ethical considerations, and outlines future trends in integrating KR&R with machine learning and large language models. This work aims to serve as a foundational reference for researchers and practitioners seeking to design robust, interpretable, and scalable intelligent systems.