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Substructural Logics: A Primer

  • Book
  • © 2002

Overview

Authors:
  1. Francesco Paoli

    1. Università di Cagliari, Italy

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Part of the book series: Trends in Logic (TREN, volume 13)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Philosophy of Substructural Logics

    1. Front Matter

      Pages 1-1
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    2. The Role of Structural Rules in Sequent Calculi

      • Francesco Paoli
      Pages 3-37

  3. The Proof Theory of Substructural Logics

    1. Front Matter

      Pages 39-39
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    2. Basic Proof Systems for Substructural Logics

      • Francesco Paoli
      Pages 41-85

    3. Cut Elimination and the Decision Problem

      • Francesco Paoli
      Pages 87-113

    4. Other Formalisms

      • Francesco Paoli
      Pages 115-155

  4. The Algebra of Substructural Logics

    1. Front Matter

      Pages 157-157
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    2. Algebraic Structures

      • Francesco Paoli
      Pages 159-197

  5. The Semantics of Substructural Logics

    1. Front Matter

      Pages 199-199
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    2. Algebraic Semantics

      • Francesco Paoli
      Pages 201-220

    3. Relational Semantics

      • Francesco Paoli
      Pages 221-255

  6. Back Matter

    Pages 257-305
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Keywords

About this book

Substructural logics are by now one of the most prominent branches of the research field usually labelled as "nonclassical logics" - and perhaps of logic tout court. Over the last few decades a vast amount of research papers and even some books have been devoted to this subject. The aim of the present book is to give a comprehensive account of the "state of the art" of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational).
Readership: This textbook is designed for a wide readership: graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics with no previous knowledge of the subject (except for a working knowledge of elementary logic) will be gradually introduced into the field starting from its basic foundations; specialists and researchers in the area will find an up-to-date survey of the most important current research topics and problems.

Reviews

From the reviews:

"This is a well written introduction to … substructural logics. … The author’s aim is to deal with a particular group of these logics … . In fact, the book could be well used as a textbook for an undergraduate course, or even for a beginning graduate course. … A further advantage of the text is that the logics are introduced in a new unified notational system making the first chapters a handy reference for any logician who works in this area of logic." (Katalin Bimbo, Mathematical Reviews, Issue 2005 b)

Authors and Affiliations

  • Università di Cagliari, Italy

    Francesco Paoli

Bibliographic Information

  • Book Title: Substructural Logics: A Primer

  • Authors: Francesco Paoli

  • Series Title: Trends in Logic

  • DOI: https://doi.org/10.1007/978-94-017-3179-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-0605-0Published: 31 May 2002

  • Softcover ISBN: 978-90-481-6014-3Published: 12 December 2011

  • eBook ISBN: 978-94-017-3179-9Published: 27 November 2013

  • Series ISSN: 1572-6126

  • Series E-ISSN: 2212-7313

  • Edition Number: 1

  • Number of Pages: XIII, 305

  • Topics: Logic, Mathematical Logic and Foundations, Order, Lattices, Ordered Algebraic Structures

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