Introduction to Mathematical Logic: Extended Edition by Michal Walicki – A Systematic Textbook on Propositional Logic, F

Introduction

Mathematical logic forms the bedrock of modern computing, artificial intelligence, and theoretical mathematics. For Indian students and researchers seeking a rigorous yet accessible foundation, Introduction to Mathematical Logic: Extended Edition by Michal Walicki offers a meticulously crafted journey through this essential discipline. Published by World Scientific Publishing Company, this hardcover edition is designed to serve both as a classroom textbook and a self-study companion for ambitious learners.

Book Overview

This extended edition presents a systematic and well-paced exploration of mathematical logic, starting from elementary set theory and progressing through computability, propositional logic, and first-order logic. Unlike conventional texts, Walicki introduces syntactic reasoning systems before diving into semantic explanations, a pedagogical approach that simplifies complex concepts. The book emphasizes the consistent reuse of logical techniques across different contexts, highlighting the unity and applicability of logical methods.

Key Highlights

• Pedagogical Innovation: Syntactic systems precede semantics, making abstract ideas more tangible for beginners.
• Comprehensive Coverage: Includes Hilbert-style and Gentzen-style reasoning systems, soundness, completeness, and decidability arguments.
• Self-Study Friendly: Requires only elementary background knowledge, suitable for Indian undergraduates and postgraduate students.
• Practical Focus: Demonstrates how logical concepts are reused across set theory, proof theory, and computability.

Inside the Book

The book opens with foundational topics: basics of set theory, mathematical induction, and an introduction to computability. It then moves into propositional logic, covering syntax, reasoning systems, and semantics. The second half delves into first-order logic, presenting both Hilbert's axiomatic system and Gentzen's natural deduction and sequent calculus. Each chapter includes worked examples, exercises, and clear explanations that bridge theory and application.

Key Topics

• Set theory fundamentals and mathematical induction
• Computability and recursive functions
• Propositional logic: syntax, semantics, and proof systems
• First-order logic: quantifiers, models, and completeness
• Hilbert and Gentzen proof systems
• Soundness, completeness, and decidability theorems

Reader Benefits

Indian students often struggle with abstract logic due to its reliance on symbolic manipulation. This book addresses that by starting with simple syntactic rules before introducing complex semantics. The extended edition includes additional material on advanced topics, making it valuable for competitive exams like GATE, NET, and university entrance tests. Researchers in mathematics, computer science, and philosophy will also find the rigorous treatment of foundational concepts indispensable.

Learning Outcomes

By working through this book, readers will gain the ability to construct formal proofs, understand the limitations of logical systems, and apply logical reasoning to real-world problems. They will master the relationship between syntax and semantics, evaluate the soundness and completeness of formal systems, and develop a deep appreciation for the elegance of mathematical logic.

Who Should Read

This book is ideal for undergraduate and postgraduate students in mathematics, computer science, and philosophy across Indian universities. It also serves self-learners preparing for research or teaching careers. Professionals in software engineering, data science, and AI who wish to strengthen their theoretical foundations will benefit greatly from its structured approach.

About the Author

Michal Walicki is a distinguished academic known for his contributions to logic and theoretical computer science. His teaching experience and research expertise shine through in this book, where complex ideas are presented with clarity and precision. Walicki’s approach reflects a deep understanding of how students learn logic, making this a trusted resource worldwide.

About the Publisher

World Scientific Publishing Company is a globally respected academic publisher specializing in high-quality science, mathematics, and technical books. With a legacy of supporting rigorous scholarship, World Scientific ensures that each title meets the highest standards of accuracy and pedagogical excellence.

Conclusion

Introduction to Mathematical Logic: Extended Edition is more than a textbook—it is a gateway to logical thinking. Whether you are a student in an Indian classroom or a researcher exploring foundational questions, this hardcover volume will equip you with the tools to reason formally, prove rigorously, and think critically. Order your copy from Bookshops.in today and begin your journey into the heart of mathematical logic.