© 2002

Substructural Logics: A Primer


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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. The Philosophy of Substructural Logics

    1. Front Matter
      Pages 1-1
  3. The Proof Theory of Substructural Logics

    1. Front Matter
      Pages 39-39
    2. Francesco Paoli
      Pages 41-85
    3. Francesco Paoli
      Pages 87-113
    4. Francesco Paoli
      Pages 115-155
  4. The Algebra of Substructural Logics

    1. Front Matter
      Pages 157-157
    2. Francesco Paoli
      Pages 159-197
  5. The Semantics of Substructural Logics

    1. Front Matter
      Pages 199-199
    2. Francesco Paoli
      Pages 201-220
    3. Francesco Paoli
      Pages 221-255
  6. Back Matter
    Pages 257-305

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.


Algebraic structure Cut-elimination theorem logic proof proof theory semantics sequent calculus

Authors and affiliations

  1. 1.Università di CagliariItaly

Bibliographic information


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)