Universal Algebraic Logic: Dedicated to the Unity of Science

This book provides a comprehensive introduction to Universal Algebraic Logic, covering universal logic, duality theories, and Tarskian algebraic logic, with applications to various logics and connections to geometry and spacetime geometry. It is suitable for both novice and experienced students.

Format: Hardback
Length: 327 pages
Publication date: 02 November 2022
Publisher: Birkhauser Verlag AG

This comprehensive textbook provides a thorough introduction to Universal Algebraic Logic. It explores three central themes:
1. Universal Logic and the Quest for Understanding: This section delves into the nature of universal logic and examines the question of what logic truly is. It discusses the relationship between different logics, including propositional logic, classical first-order logic, and other quantifier logics.
2. Duality Theories: This theme explores the connections between the world of logics and the world of algebra. It discusses duality theories that bridge the gap between these two domains, allowing for the interpretation and manipulation of logical concepts using algebraic structures.
3. Tarskian Algebraic Logic: This section focuses on Tarskian algebraic logic, including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras, and other types of algebras of logic. It covers the foundations, principles, and applications of Tarskian algebraic logic, including its connections with geometry and, ultimately, spacetime geometry.

In addition to Tarskian algebraizations of logics, the book also touches upon category theoretical perspectives. One of the notable strengths of this approach is its direct applicability to a wide range of logics, including not only propositional logics but also classical first-order logic and other quantifier logics. This versatility makes the book valuable for both novice and advanced students of logic, mathematics, and philosophy.

Furthermore, this textbook serves as a foundation for various courses designed for students with different levels of expertise. The first two chapters can be used independently as a crash course in Universal Algebra, providing a solid foundation in the subject. The subsequent chapters delve deeper into the complexities of algebraic logic, offering a comprehensive understanding of its principles and applications.

Overall, this textbook is an essential resource for anyone interested in exploring the intersection of logic, algebra, and mathematics. Its comprehensive coverage, clear explanations, and relevant examples make it an invaluable tool for students, researchers, and practitioners in the field.

Weight: 682g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031148866
Edition number: 1st ed. 2022