Mathematical Logic and AI Reasoning Foundations Formal Methods & Automated Theorem Proving VOL-1

Artificial Intelligence stands today as the most transformative force in the modern world—driving innovation in industries, research, computational sciences, robotics, business, healthcare, cybersecurity, automation, education, and complex decision-making environments. At the core of these revolutionary technologies lies a discipline that has shaped human thinking for more than two thousand years: Mathematical Logic. It is the formal, structured, and precise language through which intelligent machines reason, infer, prove, validate, and construct meaningful knowledge. As AI systems advance from mere data-driven models to explainable, interpretable, and logic-grounded intelligent agents, the need to understand mathematical logic and automated reasoning becomes essential for students, researchers, engineers, and professionals worldwide.This book, “Mathematical Logic and AI Reasoning: Foundations, Automated Proofs & Intelligent Inference,” authored by Anshuman Mishra, is an extensive and modern exploration of logic-based artificial intelligence. It is written for those who wish to master the foundations of logic and the intelligent reasoning mechanisms that power today’s theorem provers, SAT/SMT solvers, symbolic AI engines, and hybrid neuro-symbolic learning systems.Whether you are a student learning logic, a researcher advancing AI reasoning, or a professional applying logic-based techniques to real-world systems, this book provides a clear, rigorous, practical, and deeply insightful journey from fundamental concepts to advanced AI-level reasoning.WHY THIS BOOK?AI systems are no longer limited to numerical optimization and statistical learning alone. The future belongs to machines that can reason, explain, justify, and prove. From self-driving cars that perform symbolic planning to financial systems that validate rules using automated solvers, from intelligent legal assistants performing logical inference to verification tools guaranteeing software correctness—logic is everywhere.This book bridges the gap between mathematical logic, theoretical computer science, and modern AI reasoning. It is designed to be both an academic textbook and an industrial handbook.WHAT THIS BOOK OFFERS1. A Complete Foundation in Mathematical LogicReaders begin with the fundamentals—propositional logic and predicate logic—learning the essential language of reasoning used in mathematics and artificial intelligence. The book covers:Syntax and semantics of logical languagesTruth tables, connectives, formulas, and valuationsNormal forms (CNF, DNF, Prenex forms)Quantifiers, predicates, functions, and structuresLogical equivalence, entailment, validity, and satisfiabilitySoundness, completeness, and consistencyThe treatment is intuitive yet mathematically rigorous, suitable for undergraduate students and advanced researchers alike.2. Automated Reasoning & Theorem Proving TechniquesOne of the core contributions of this book is its detailed coverage of automated theorem proving—the heart of symbolic AI. Topics include:Natural deductionSequent calculusTableaux and semantic treesUnification and resolutionHerbrand’s Theorem and Herbrand universeTerm rewriting and substitutionResolution-based FOL theorem provingThe explanations are accompanied by step-by-step examples, logical diagrams, proof trees, and real-case reasoning problems.3. SAT, SMT & Modern AI SolversThe book introduces readers to the technology behind:SAT solversSMT solversDPLL and CDCL algorithmsZ3, CVC5, and Prolog-based reasoningConstraint solving Read more