Overview
- Presents an introduction to the algebraic study of non-classical logics
- Details a powerful methodology to understand logics with implication
- Includes many particular logics as examples for the theory
Part of the book series: Trends in Logic (TREN, volume 57)
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Table of contents (7 chapters)
Keywords
- Non-Classical Logics
- Algebraic Logic
- Abstract Algebraic Logic
- Propositional Logic
- Predicate Logic
- Logical Connectives
- Completeness Theorems
- Algebraic Semantics
- Logical Matrices
- Weakly Implicative Logics
- Substructural Logics
- Generalized Disjunctions
- Semilinear Logics
- First-Order Predicate Logics
- implication and disjunction in logics
- logics and their algebraic semantics
About this book
This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions.
Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics.
The bookmay be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.
Authors and Affiliations
About the authors
Petr Cintula is a senior researcher at the Institute of Computer Science of the Czech Academy of Sciences. He is co-author of over 60 publications mainly on mathematical fuzzy logic and abstract algebraic logic. Furthermore, he has co-edited the three volumes of Handbook of Mathematical Fuzzy Logic and has been principal (co-)investigator of numerous research projects.
Carles Noguera is a senior researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences, where he has led several research projects on topics of mathematical fuzzy logic, many-valued logics, and abstract algebraic logic. He obtained his degrees in Mathematics and Philosophy and a PhD in Logic at the University of Barcelona.
Bibliographic Information
Book Title: Logic and Implication
Book Subtitle: An Introduction to the General Algebraic Study of Non-classical Logics
Authors: Petr Cintula, Carles Noguera
Series Title: Trends in Logic
DOI: https://doi.org/10.1007/978-3-030-85675-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-85674-8Published: 27 November 2021
Softcover ISBN: 978-3-030-85677-9Published: 28 November 2022
eBook ISBN: 978-3-030-85675-5Published: 01 January 2022
Series ISSN: 1572-6126
Series E-ISSN: 2212-7313
Edition Number: 1
Number of Pages: XXII, 465
Number of Illustrations: 17 b/w illustrations
Topics: Logic, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages