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Sequents and Trees

An Introduction to the Theory and Applications of Propositional Sequent Calculi

  • Textbook
  • © 2021

Overview

Authors:
  1. Andrzej Indrzejczak

    1. Institute of Philosophy, University of Łódź, Lodz, Poland

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  • 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.

Part of the book series: Studies in Universal Logic (SUL)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Analytic Sequent Calculus for CPL

    • Andrzej Indrzejczak
    Pages 1-61

  3. Gentzen’s Sequent Calculus LK

    • Andrzej Indrzejczak
    Pages 63-112

  4. Purely Logical Sequent Calculus

    • Andrzej Indrzejczak
    Pages 113-162

  5. Sequent Calculi for Modal Logics

    • Andrzej Indrzejczak
    Pages 163-242

  6. Alternatives to CPL

    • Andrzej Indrzejczak
    Pages 243-299

  7. Back Matter

    Pages 301-345
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Keywords

About this book

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, andapplied 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.


Reviews

“Each chapter of the book is structured in a similar way and contains the basic definitions, facts and necessary discussion regarding the key notions, accompanied with new ideas and a wide reference list, followed by the author's clear and approachable style. This book is self-contained, presenting an extensive survey of the applications and usefulness of cut elimination, and seems to be an extremely interesting source not only for logicians and philosophers, but also for researchers in computer science.” (Branislav Boričić, Mathematical Reviews, May, 2022)

Authors and Affiliations

  • Institute of Philosophy, University of Łódź, Lodz, Poland

    Andrzej Indrzejczak

About the author

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).

Bibliographic Information

  • 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

  • DOI: https://doi.org/10.1007/978-3-030-57145-0

  • Publisher: Birkhäuser 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 2021

  • Hardcover ISBN: 978-3-030-57144-3Published: 17 December 2020

  • Softcover ISBN: 978-3-030-57147-4Published: 18 December 2021

  • eBook ISBN: 978-3-030-57145-0Published: 16 December 2020

  • Series ISSN: 2297-0282

  • Series E-ISSN: 2297-0290

  • Edition Number: 1

  • Number of Pages: XVI, 345

  • Number of Illustrations: 14 b/w illustrations, 1 illustrations in colour

  • Topics: Structures and Proofs, Logic, Philosophy of Mathematics

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