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Residuated Structures in Algebra and Logic
 
George Metcalfe University of Bern, Bern, Switzerland
Francesco Paoli University of Cagliari, Cagliari, Italy
Constantine Tsinakis Vanderbilt University, Nashville, TN
Softcover ISBN:  978-1-4704-6985-6
Product Code:  SURV/277
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7551-2
Product Code:  SURV/277.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6985-6
eBook: ISBN:  978-1-4704-7551-2
Product Code:  SURV/277.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
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Residuated Structures in Algebra and Logic
George Metcalfe University of Bern, Bern, Switzerland
Francesco Paoli University of Cagliari, Cagliari, Italy
Constantine Tsinakis Vanderbilt University, Nashville, TN
Softcover ISBN:  978-1-4704-6985-6
Product Code:  SURV/277
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7551-2
Product Code:  SURV/277.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-6985-6
eBook ISBN:  978-1-4704-7551-2
Product Code:  SURV/277.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2772023; 265 pp
    MSC: Primary 03; 06;

    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.

    Readership

    Graduate students and researchers interested in formal mathematical logic.

  • Table of Contents
     
     
    • Chapters
    • Order and residuation
    • Proof systems
    • Consequence relations
    • Structure theory
    • Semilinearity and distributivity
    • Cancellativity
    • Divisibility
    • Bridges between algebra and logic
    • Finite embeddings and finite models
    • Open problems
    • Basic notions of universal algebra
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2772023; 265 pp
MSC: Primary 03; 06;

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.

Readership

Graduate students and researchers interested in formal mathematical logic.

  • Chapters
  • Order and residuation
  • Proof systems
  • Consequence relations
  • Structure theory
  • Semilinearity and distributivity
  • Cancellativity
  • Divisibility
  • Bridges between algebra and logic
  • Finite embeddings and finite models
  • Open problems
  • Basic notions of universal algebra
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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