Formal Logic

Why do some statements necessarily imply others - and why do even the strongest formal systems have limits? Logic offers the tools to explore these questions with precision, clarity, and depth. This book provides a rigorous yet accessible introduction to logical reasoning, from propositional and predicate logic to modal logic and non-classical logics. It presents the essential concepts, methods, and procedures in a clear and structured way, with attention not only to formal systems but also to structure, meaning, and inference. Classical topics such as equivalences, normal forms, and resolution are complemented by algorithmic methods for automated reasoning and a detailed treatment of Gödel's incompleteness theorems. Modern perspectives, including modal logic, fuzzy logic, default logic, and answer set programming, round out the presentation. With numerous exercises and carefully worked solutions, this book is ideal for students and readers who want to think more clearly, argue more precisely, and gain a deeper understanding of the foundations of mathematics and computer science.