Mathematical Logic and AI Reasoning

Advanced Knowledge Representation, Logic Programming & Intelligent Automated Reasoning (Vol. 2)

Modern Artificial Intelligence has evolved far beyond simple rule-based systems. Today’s intelligent systems combine formal logic, automated theorem proving, knowledge representation, neural-symbolic reasoning, formal verification, and large language models to solve complex real-world problems.

Mathematical Logic and AI Reasoning: Advanced Knowledge Representation, Logic Programming & Intelligent Automated Reasoning (Vol. 2) continues the journey from Volume 1 by exploring advanced logical reasoning techniques used in modern Artificial Intelligence, software verification, robotics, knowledge engineering, natural language understanding, and explainable AI.

This volume provides a comprehensive treatment of SAT solvers, SMT solvers, Description Logic, Ontologies, Semantic Networks, Intelligent Agents, Logic Programming, PROLOG, Neural-Symbolic AI, Inductive Logic Programming, Formal Verification, Model Checking, and AI-assisted Theorem Proving.

Readers will learn how mathematical logic enables machines to reason, verify software correctness, represent complex knowledge, automate decision-making, and support trustworthy Artificial Intelligence systems. The book combines rigorous mathematical concepts with practical AI applications and modern research trends, making it valuable for both academic study and industrial development.

Whether you are a graduate student, AI researcher, software engineer, robotics developer, or formal methods specialist, this volume provides an advanced foundation for intelligent reasoning and computational logic.

What You’ll Learn

✔ Satisfiability Problem (SAT)

✔ SAT Solvers

✔ DPLL Algorithm

✔ Conflict-Driven Clause Learning (CDCL)

✔ MiniSAT

✔ Glucose Solver

✔ Kissat Solver

✔ Satisfiability Modulo Theories (SMT)

✔ Z3 Theorem Prover

✔ CVC5 Solver

✔ Software Verification

✔ AI Planning

✔ Knowledge Representation

✔ Semantic Networks

✔ Description Logic

✔ Ontology Engineering

✔ OWL

✔ RDF

✔ Rule-Based Systems

✔ Logic-Based Systems

✔ Fuzzy Logic

✔ Modal Logic

✔ Temporal Logic

✔ Linear Temporal Logic (LTL)

✔ Computational Tree Logic (CTL)

✔ Intuitionistic Logic

✔ Paraconsistent Logic

✔ Bayesian Logic

✔ Probabilistic Reasoning

✔ Logic-Based Intelligent Agents

✔ Constraint Satisfaction Problems (CSP)

✔ STRIPS Planning

✔ GraphPlan

✔ Game Playing AI

✔ Cognitive Architectures

✔ SOAR

✔ ACT-R

✔ Natural Language Semantic Parsing

✔ Logic Programming

✔ PROLOG Programming

✔ Unification Algorithms

✔ Backtracking Search

✔ Definite Clause Grammars (DCG)

✔ Neural-Symbolic AI

✔ Differentiable Logic

✔ Inductive Logic Programming (ILP)

✔ Graph Neural Networks

✔ Explainable Artificial Intelligence (XAI)

✔ Formal Verification

✔ Model Checking

✔ Symbolic Verification

✔ Binary Decision Diagrams (BDD)

✔ AI-Based Proof Assistants

✔ Large Language Models for Logical Reasoning

✔ Automated Theorem Proving

✔ AI Safety

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:

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

Key Features

✅ Advanced Mathematical Logic for Artificial Intelligence

✅ SAT, SMT, and Automated Theorem Proving

✅ Knowledge Representation and Ontology Engineering

✅ Intelligent Agents and AI Planning

✅ Logic Programming using PROLOG

✅ Neural-Symbolic Artificial Intelligence

✅ Explainable AI and Hybrid Reasoning

✅ Formal Verification and Model Checking

✅ Large Language Models for Logical Reasoning

✅ AI Safety and Trustworthy Artificial Intelligence

✅ Industry-oriented case studies

✅ Suitable for research, graduate studies, and professional development

Why This Book?

Artificial Intelligence increasingly depends on formal reasoning, symbolic knowledge, software verification, and explainable decision-making. While many AI books emphasize machine learning algorithms, they often overlook the logical foundations required to build reliable, interpretable, and verifiable intelligent systems.

This book fills that gap by presenting a unified framework that combines mathematical logic, automated reasoning, knowledge representation, formal verification, and AI planning. Readers gain both theoretical insight and practical skills for designing intelligent systems capable of reasoning, proving, verifying, and making trustworthy decisions.

From SAT solvers and PROLOG programming to neural-symbolic AI, model checking, and large language model reasoning, this volume prepares readers for advanced research and industrial applications in next-generation Artificial Intelligence.

Book Details

Title: Mathematical Logic and AI Reasoning

Subtitle: Advanced Knowledge Representation, Logic Programming & Intelligent Automated Reasoning

Volume: Vol. 2

Author: Anshuman Mishra

Publisher: Anshuman Mishra

Publication Year: 2025

Language: English

Category: Artificial Intelligence, Mathematical Logic, Automated Reasoning, Knowledge Representation, Computer Science, Formal Methods

Binary Decision Diagrams

Mathematical Logic and AI Reasoning VOL-2