Mathematical Logic and AI Reasoning

Foundations, Formal Methods & Automated Theorem Proving (Vol. 1)

Logic has always been the foundation of mathematical reasoning, scientific thinking, and computational intelligence. In the modern era of Artificial Intelligence (AI), Machine Learning, Robotics, Knowledge Representation, Expert Systems, Formal Verification, and Automated Reasoning, mathematical logic plays an even more significant role by enabling machines to reason, infer, verify, and make intelligent decisions.

Mathematical Logic and AI Reasoning: Foundations, Formal Methods & Automated Theorem Proving (Vol. 1) provides a comprehensive introduction to formal logic and demonstrates how logical reasoning forms the backbone of intelligent systems. The book combines classical mathematical logic with modern Artificial Intelligence applications, making abstract concepts accessible through structured explanations, practical examples, and real-world case studies.

Beginning with the fundamentals of logic, syntax, semantics, propositional logic, and predicate logic, the book gradually progresses toward proof systems, inference algorithms, model theory, knowledge representation, automated reasoning, SAT solvers, SMT solvers, theorem proving, and AI reasoning systems.

Readers will develop a deep understanding of how intelligent machines perform logical inference, verify correctness, solve complex reasoning problems, and automate mathematical proofs using modern computational techniques.

Whether you are a university student, researcher, software engineer, AI developer, mathematician, or educator, this book provides an excellent foundation in formal logic and its applications across Artificial Intelligence and Computer Science.

What You’ll Learn

✔ Foundations of Mathematical Logic

✔ Logic for Artificial Intelligence

✔ Syntax and Semantics

✔ Logical Arguments

✔ Validity and Soundness

✔ Deductive Reasoning

✔ Proof Theory

✔ Boolean Algebra

✔ Set Theory

✔ Machine Intelligence

✔ Robotics Reasoning

✔ Propositional Logic

✔ Logical Connectives

✔ Truth Tables

✔ Tautologies

✔ Conjunctive Normal Form (CNF)

✔ Disjunctive Normal Form (DNF)

✔ Logical Equivalence

✔ Logical Implication

✔ Resolution Method

✔ Predicate Logic

✔ First-Order Logic (FOL)

✔ Quantifiers

✔ Functions and Predicates

✔ Free and Bound Variables

✔ Prenex Normal Form

✔ Skolemization

✔ Knowledge Graphs

✔ Formal Proof Systems

✔ Natural Deduction

✔ Sequent Calculus

✔ Semantic Tableaux

✔ Mathematical Induction

✔ Proof by Contradiction

✔ Forward Chaining

✔ Backward Chaining

✔ Unification Algorithm

✔ Clause Form Conversion

✔ Horn Clauses

✔ Logic Programming

✔ Herbrand Models

✔ Model Theory

✔ Formal Semantics

✔ Satisfiability

✔ Logical Entailment

✔ Model Checking

✔ Automated Reasoning

✔ Automated Theorem Proving

✔ SAT Solvers

✔ SMT Solvers

✔ Coq

✔ Isabelle

✔ Prolog

✔ Z3 Theorem Prover

Part I – Introduction to Mathematical Logic

Chapter 1

Fundamentals of Logic

Chapter 2

Propositional Logic

Chapter 3

Predicate Logic (First-Order Logic)

Part II – Formal Proof Systems & Inference

Chapter 4

Proof Techniques

Chapter 5

Logical Inference Algorithms

Chapter 6

Model Theory & Formal Semantics

Part III – Automated Reasoning & AI Proof Systems

Chapter 7

Automated Reasoning Fundamentals

Chapter 8

Theorem Proving Techniques

Who Should Read This Book?

This book is ideal for:

B.Tech Students
BCA Students
MCA Students
B.Sc. Computer Science Students
M.Tech Students
Artificial Intelligence Students
Machine Learning Students
Computer Science Students
Mathematics Students
Software Engineers
AI Engineers
Knowledge Engineers
Robotics Researchers
Formal Methods Researchers
Cybersecurity Researchers
Research Scholars
University Faculty
Competitive Examination Aspirants
Logic Programming Enthusiasts
Automated Reasoning Researchers

Key Features

✅ Comprehensive introduction to Mathematical Logic

✅ AI-oriented explanation of formal reasoning

✅ Covers Propositional and Predicate Logic

✅ Step-by-step proof techniques

✅ Automated reasoning algorithms

✅ Knowledge Representation and Logic Programming

✅ SAT and SMT Solver fundamentals

✅ Modern AI reasoning systems

✅ Research-oriented and industry-relevant content

✅ University syllabus aligned

✅ Ideal for self-study, research, and professional learning

Why This Book?

While many textbooks teach mathematical logic as a purely theoretical subject, Mathematical Logic and AI Reasoning demonstrates how formal logic serves as the foundation of modern Artificial Intelligence, automated reasoning, expert systems, formal verification, and intelligent decision-making.

The book integrates mathematical rigor with practical AI applications, enabling readers to understand how logical inference, theorem proving, and formal verification are applied in robotics, software verification, knowledge graphs, planning systems, databases, and intelligent agents.

Whether you are preparing for university examinations, conducting AI research, building intelligent systems, or studying formal methods, this book provides a complete guide to the mathematical principles underlying modern computational reasoning.

Book Details

Title: Mathematical Logic and AI Reasoning

Subtitle: Foundations, Formal Methods & Automated Theorem Proving

Volume: Vol. 1

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Category: Artificial Intelligence, Mathematical Logic, Computer Science, Formal Methods, Automated Reasoning, Theorem Proving

Coq

Mathematical Logic and AI Reasoning VOL-1