About the Book

Mathematical Logic and AI Reasoning: Foundations, Formal Methods & Automated Theorem Proving (Vol-I)

Artificial Intelligence is entering a new era—an era where machines are expected not only to learn from data but also to reason, explain, verify, justify, and make logically sound decisions. While machine learning and deep learning have revolutionized pattern recognition, true intelligence requires something deeper: the ability to perform structured reasoning.

At the heart of this capability lies Mathematical Logic.

Mathematical Logic and AI Reasoning: Foundations, Formal Methods & Automated Theorem Proving (Vol-I) provides a comprehensive and modern exploration of logic as the foundation of intelligent systems. This book bridges classical mathematical logic, theoretical computer science, automated reasoning, formal verification, symbolic AI, and modern knowledge-based systems into a unified framework designed for the next generation of AI practitioners and researchers.

Beginning with the fundamentals of propositional and predicate logic, the book gradually develops the formal machinery required to understand inference, proof systems, theorem proving, satisfiability, knowledge representation, and intelligent reasoning. Readers learn not only how logical systems are constructed but also how they power modern AI applications including planning systems, expert systems, theorem provers, software verification tools, intelligent agents, and hybrid neuro-symbolic architectures.

The book covers:

• Foundations of propositional and first-order logic
• Formal proof systems and inference mechanisms
• Resolution methods and unification algorithms
• Automated theorem proving techniques
• SAT and SMT solvers
• Knowledge representation and ontologies
• Logic programming and Prolog
• Non-classical logics including fuzzy, modal, temporal, and probabilistic logic
• Intelligent agents and reasoning systems
• Formal verification and model checking
• Neural-symbolic AI and explainable reasoning
• Emerging research directions in logic-based artificial intelligence

Unlike traditional logic textbooks that focus exclusively on mathematical theory, this volume continuously connects logic to real-world AI systems. Readers discover how automated reasoning supports software correctness, robotics, cybersecurity, planning, natural language understanding, decision support systems, and trustworthy AI.

The book is designed for undergraduate and postgraduate students, researchers, faculty members, AI engineers, software developers, and professionals seeking a rigorous yet practical understanding of machine reasoning.

Every chapter combines theoretical foundations with examples, proof techniques, algorithms, diagrams, and case studies, enabling readers to move confidently from abstract logic to real-world intelligent systems.

As the future of AI increasingly demands explainability, safety, transparency, and formal guarantees, mathematical logic is becoming more important than ever. This book equips readers with the tools necessary to understand, design, and evaluate intelligent systems capable of reasoning with precision and reliability.

More than a textbook, this work serves as a roadmap toward the future of explainable, verifiable, and trustworthy artificial intelligence.