Basic Proof Theory

This book provides a thorough introduction to structural proof theory, exploring its applications in logic and computer science. Basic Proof Theory is ideal for graduate students.

This text serves as a comprehensive introduction to the foundational concepts of structural proof theory. In this new edition of Basic Proof Theory, several sections have been rewritten to enhance clarity, and new content has been included, particularly focusing on cut elimination. Additionally, solutions to selected exercises have been provided, making it easier for readers to engage with the material. The book offers a thorough discussion of various formalizations of first-order logic, allowing readers to grasp the nuances of the subject matter.

Throughout Basic Proof Theory, examples are drawn from various application areas, including the metamathematics of both intuitionistic and classical first-order logic, logic programming, category theory, modal logic, linear logic, first-order arithmetic, and second-order logic. Each example is designed to illustrate the methods in relatively straightforward contexts before progressing to more complex scenarios. This structured approach ensures that readers can build a solid foundation before tackling more intricate applications.

The text is peppered with numerous exercises that encourage active learning. It is primarily geared towards graduate students and early-stage researchers in fields such as mathematical logic, theoretical computer science, and artificial intelligence. With only a standard course in first-order logic as a prerequisite, Basic Proof Theory is an accessible resource for those looking to deepen their understanding of proof theory and its applications.