Sequents and Trees
An Introduction to the Theory and Applications of Propositional Sequent Calculi
Authors: Indrzejczak, Andrzej
Free Preview- Considers the methodology and techniques of sequent calculus to illustrate its use in proving a wide range of metatheoretical results
- Includes many results and their proofs that are often not well known or easily accessible
- Examines important and nonstandard generalized sequent calculi, like hypersequent and structured sequent calculi.
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- About this Textbook
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This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus.
After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics.
Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers. - About the authors
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Andrzej Indrzejczak is a logician working on the problems of proof theory and its applications to non-classical logics. He is an author of several papers on natural deduction and sequent systems for modal and temporal logics, and of the monograph Natural Deduction, Hybrid Systems and Modal Logics (Springer, 2010).
- Table of contents (5 chapters)
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Analytic Sequent Calculus for CPL
Pages 1-61
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Gentzen’s Sequent Calculus LK
Pages 63-112
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Purely Logical Sequent Calculus
Pages 113-162
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Sequent Calculi for Modal Logics
Pages 163-242
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Alternatives to CPL
Pages 243-299
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Sequents and Trees
- Book Subtitle
- An Introduction to the Theory and Applications of Propositional Sequent Calculi
- Authors
-
- Andrzej Indrzejczak
- Series Title
- Studies in Universal Logic
- Copyright
- 2021
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-57145-0
- DOI
- 10.1007/978-3-030-57145-0
- Hardcover ISBN
- 978-3-030-57144-3
- Series ISSN
- 2297-0282
- Edition Number
- 1
- Number of Pages
- XVI, 345
- Number of Illustrations
- 14 b/w illustrations, 1 illustrations in colour
- Topics
