Overview
- Is the first monograph ever on logics of variable inclusion
- Highly relevant to logicians, philosophers and algebraists alike
- Puts together two separate research streams, in logic and algebra respectively
Part of the book series: Trends in Logic (TREN, volume 59)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
- Many-valued Logics
- Logics of Variable Inclusion
- Significance Logics
- Kleene Logics
- Nonclassical Logics
- Regular Varieties
- Plonka Sums
- Bisemilattices
- Abstract Algebraic Logic
- Universal Algebra
- Analyticity, Consequence, and Meaninglessness
- Płonka Sums and Regular Varieties
- Dualities for Regular Varieties
- Logics of Left Variable Inclusion
- Logics of Right Variable Inclusion
- Paraconsistent Weak Kleene Logic
About this book
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.
Reviews
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Logics of Variable Inclusion
Authors: Stefano Bonzio, Francesco Paoli, Michele Pra Baldi
Series Title: Trends in Logic
DOI: https://doi.org/10.1007/978-3-031-04297-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-04296-6Published: 10 June 2022
Softcover ISBN: 978-3-031-04299-7Published: 10 June 2023
eBook ISBN: 978-3-031-04297-3Published: 09 June 2022
Series ISSN: 1572-6126
Series E-ISSN: 2212-7313
Edition Number: 1
Number of Pages: X, 221
Number of Illustrations: 4 b/w illustrations
Topics: Logic, Mathematical Logic and Foundations, Philosophy, general