Artificial intelligence is often associated with machine learning, neural networks, and massive datasets. Yet beneath these powerful technologies lies a more fundamental question: how do intelligent systems reason?
This volume explores the mathematical foundations of reasoning itself. It introduces the logical principles that allow knowledge to be represented, organized, verified, and transformed into conclusions through formal deduction. In doing so, it reveals why logic remains one of the most essential pillars of computer science and symbolic artificial intelligence.
Beginning with knowledge representation and symbolic reasoning, the book establishes the conceptual framework through which intelligent systems describe facts, rules, relationships, and decisions. It then develops the formal tools of propositional logic, Boolean algebra, Boolean equation systems, and logical functions, progressively showing how reasoning can be expressed with mathematical precision.
Building upon these foundations, the reader is introduced to deductive inference, formal proofs, resolution methods, automated theorem proving, and the mechanisms through which machines can derive conclusions from explicit knowledge. The final chapters explore rule-based reasoning, inference engines, forward and backward chaining, and expert systems, demonstrating how logical principles become operational components of intelligent systems.
Throughout the book, mathematical rigor is combined with practical applications drawn from computer science, artificial intelligence, cybersecurity, decision-support systems, automated reasoning, and knowledge engineering. Numerous examples, exercises, and detailed solutions guide the reader from fundamental concepts to advanced reasoning techniques while maintaining a strong connection to real-world intelligent systems.
More than a traditional logic textbook, this volume presents logic as a living technology of reasoning; one that enables machines to explain decisions, verify conclusions, manipulate knowledge, and support human problem solving.
Designed for students, educators, researchers, software engineers, and artificial intelligence professionals, this book provides a comprehensive introduction to the logical foundations upon which trustworthy, explainable, and knowledge-driven intelligent systems are built.
Mathematical Logic and Symbolic Reasoning for Artificial Intelligence is the second volume of The Mathematics for Computer Science and Symbolic Artificial Intelligence Series, a collection dedicated to the mathematical structures that underpin modern computing and intelligent systems
