Mathematical Logic and AI Reasoning

Advanced Automated Theorem Proving, Knowledge Representation & Intelligent Inference (Vol. 2)

As Artificial Intelligence evolves beyond statistical learning toward explainable, trustworthy, and reasoning-driven systems, logical inference, formal verification, automated theorem proving, and symbolic reasoning have become indispensable technologies. Intelligent systems today must not only learn from data but also reason, explain decisions, verify correctness, and interact safely with humans in critical environments.

Mathematical Logic and AI Reasoning: Advanced Automated Theorem Proving, Knowledge Representation & Intelligent Inference (Vol. 2) extends the mathematical foundations established in Volume 1 and presents modern developments in symbolic Artificial Intelligence, automated reasoning, SAT/SMT solving, intelligent agents, knowledge representation, logic programming, formal verification, and neuro-symbolic AI.

Readers will gain a deep understanding of SAT solvers, SMT solvers, DPLL and CDCL algorithms, Z3 and CVC5, Description Logics, OWL and RDF ontologies, Fuzzy Logic, Modal Logic, Temporal Logic, Bayesian Logic, intelligent agents, planning algorithms, Prolog programming, neural-symbolic learning, explainable AI, formal verification, model checking, and AI-assisted theorem proving.

The book combines rigorous mathematical theory with practical AI applications, real-world case studies, software verification techniques, and emerging research in Large Language Models, symbolic reasoning, and AI proof assistants.

Designed for postgraduate students, PhD scholars, university faculty, AI researchers, software engineers, robotics developers, cybersecurity professionals, and computational logicians, this volume serves as a comprehensive reference for advanced logic-based Artificial Intelligence.

What You’ll Learn

✔ SAT (Boolean Satisfiability) Problem

✔ SAT Solvers

✔ SMT Solvers

✔ DPLL Algorithm

✔ Conflict-Driven Clause Learning (CDCL)

✔ MiniSAT

✔ Glucose Solver

✔ Kissat Solver

✔ Z3 Solver

✔ CVC5 Solver

✔ Software Verification

✔ AI Planning

✔ Knowledge Representation (KR)

✔ Semantic Networks

✔ Description Logic (DL)

✔ Ontologies

✔ OWL

✔ RDF

✔ Rule-Based Systems

✔ Logic-Based Expert Systems

✔ Fuzzy Logic

✔ Modal Logic

✔ Temporal Logic (LTL & CTL)

✔ Intuitionistic Logic

✔ Paraconsistent Logic

✔ Bayesian Logic

✔ Probabilistic Logic

✔ AI Safety

✔ Intelligent Agents

✔ STRIPS Planning

✔ Graphplan Algorithm

✔ Constraint Satisfaction Problems (CSP)

✔ Cognitive Architectures (SOAR & ACT-R)

✔ Semantic Parsing

✔ Logic Programming

✔ Prolog Programming

✔ Unification

✔ Backtracking Algorithms

✔ Definite Clause Grammars

✔ Neural-Symbolic Artificial Intelligence

✔ Differentiable Logic

✔ Inductive Logic Programming (ILP)

✔ Graph Neural Networks

✔ Explainable AI (XAI)

✔ Formal Verification

✔ Model Checking

✔ Large Language Models (LLMs)

✔ AI Proof Assistants

✔ Automated Reasoning Research

Chapter 9

SAT & SMT Solvers in Artificial Intelligence

Part IV – Knowledge Representation & AI Reasoning

Chapter 10

Logic in Knowledge Representation

Chapter 11

Non-Classical & Advanced Logic

Chapter 12

AI Reasoning Systems & Intelligent Agents

Part V – Advanced Topics for Researchers

Chapter 13

Logic Programming & PROLOG

Chapter 14

Machine Learning Meets Logic

Chapter 15

Formal Verification & Model Checking

Chapter 16

Research Frontiers in Automated Reasoning

Who Should Read This Book?

This book is ideal for:

M.Tech Students
PhD Scholars
Artificial Intelligence Researchers
Machine Learning Engineers
Symbolic AI Researchers
Software Engineers
Robotics Engineers
Cybersecurity Professionals
Formal Verification Engineers
Compiler Developers
Logic Programming Enthusiasts
Explainable AI Researchers
Data Scientists
Knowledge Engineers
NLP Researchers
Computer Science Faculty
Research Scientists
Intelligent Systems Developers
University Students
Competitive Examination Aspirants

Key Features

✅ Comprehensive coverage of SAT and SMT solving techniques

✅ Practical introduction to Z3, CVC5, MiniSAT, Glucose, and Kissat

✅ Advanced Knowledge Representation and Ontology Engineering

✅ Non-Classical Logics for modern Artificial Intelligence

✅ Logic Programming with Prolog

✅ Neural-Symbolic Artificial Intelligence and Explainable AI

✅ Formal Verification and Model Checking

✅ Applications in Robotics, Software Verification, Cybersecurity, and Autonomous Systems

✅ Research-oriented content covering LLMs and AI-assisted theorem proving

✅ Industry-relevant examples and practical case studies

✅ Suitable for postgraduate education, advanced AI research, and industrial applications

Why This Book?

The future of Artificial Intelligence depends on systems that are not only intelligent but also explainable, verifiable, trustworthy, and logically consistent. While statistical machine learning has achieved remarkable success, many real-world applications—including autonomous vehicles, aerospace, finance, healthcare, cybersecurity, and robotics—require formal reasoning and mathematical guarantees.

This volume bridges the gap between classical mathematical logic and next-generation AI technologies by integrating symbolic reasoning, automated theorem proving, formal verification, knowledge representation, SAT/SMT solving, logic programming, and neural-symbolic learning into one comprehensive framework.

Readers will discover how logical reasoning powers expert systems, intelligent agents, software verification tools, planning algorithms, Large Language Models, and Explainable AI while gaining practical knowledge of modern theorem provers and verification frameworks used in academia and industry.

Whether you are conducting AI research, designing reasoning systems, building intelligent software, or studying formal methods, this book provides an authoritative guide to advanced logic-based Artificial Intelligence.

Book Details

Title: Mathematical Logic and AI Reasoning

Subtitle: Advanced Automated Theorem Proving, Knowledge Representation & Intelligent Inference

Volume: Vol. 2

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Category: Artificial Intelligence, Mathematical Logic, Symbolic AI, Automated Reasoning, Formal Methods, Computer Science

AI Proof Assistants

Mathematical Logic and AI Reasoning VOL-2