Residuated Structures in Algebra and Logic (Paperback)

George Metcalfe

ISBN 10: 1470469855 / ISBN 13: 9781470469856

Published by American Mathematical Society, Providence, 2023

About this Item

Paperback. This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures.The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field. An introduction to residuated structures, a common thread binding together algebra and logic, designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781470469856

Bibliographic Details

• Title: Residuated Structures in Algebra and Logic (Paperback)
• Publisher: American Mathematical Society, Providence
• Publication Date: 2023
• Language: English
• ISBN 10: 1470469855
• ISBN 13: 9781470469856
• Binding: Paperback
• Condition: new

About this title

Synopsis

This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

About the Author

George Metcalfe, University of Bern, Switzerland, Francesco Paoli, University of Cagliari, Italy, and Constantine Tsinakis, Vanderbilt University, Nashville, TN