Logics of Variable Inclusion: 59 (Trends in Logic, 59) - Hardcover

Bonzio, Stefano; Paoli, Francesco; Pra Baldi, Michele

Hardcover

ISBN 10: 3031042964 ISBN 13: 9783031042966

Publisher: Springer, 2022

Synopsis

This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.

The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.

About this title

About the Author

Stefano Bonzio is assistant professor of Mathematical Logic at the University of Cagliari, where he teaches Algebra and Discrete Mathematics. He is author of more than 20 publications in international peer-reviewed journals. His research interests include non-classical logics (in particular Kleene logics), algebraic logic and universal algebra, the foundation of probability.

Francesco Paoli is a full professor of Logic at the University of Cagliari. He published, among other things, the book Substructural Logics: A Primer (Kluwer, 2002) and over 60 papers in international peer-reviewed journals. His research interests include nonclassical (substructural, quantum, many-valued) logics, universal algebra, and the foundations of physics.

Michele Pra Baldi is a post-doctoral researcher at the Artificial Intelligence Research Institute, Spanish National Council of Research (Bellaterra, Barcelona, Spain). He obtained his PhD at the University of Padua in 2019. His research interests include abstract algebraic logic, universal algebra, non-classical logics and their applications to formal epistemology and philosophical logic.

From the Back Cover

This monograph shows that, through a recourse to the concepts and methods of abstract algebraic logic, the algebraic theory of regular varieties and the concept of analyticity in formal logic can profitably interact. By extending the technique of Plonka sums from algebras to logical matrices, the authors investigate the different classes of models for logics of variable inclusion and they shed new light into their formal properties.

The book opens with the historical origins of logics of variable inclusion and on their philosophical motivations. It includes the basics of the algebraic theory of regular varieties and the construction of Plonka sums over semilattice direct systems of algebra. The core of the book is devoted to an abstract definition of logics of left and right variable inclusion, respectively, and the authors study their semantics using the construction of Plonka sums of matrix models. The authors also cover Paraconsistent Weak Kleene logic and survey its abstract algebraic logical properties. This book is of interest to scholars of formal logic.

Edition details

• Publisher: Springer
• Publication date: 2022
• Language: English
• ISBN 10: 3031042964
• ISBN 13: 9783031042966
• Binding: Hardcover
• Edition number: 1
• Number of pages: 231