Advertisement

Displaying Modal Logic

  • Heinrich Wansing

Part of the Trends in Logic book series (TREN, volume 3)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Heinrich Wansing
    Pages 1-14
  3. Heinrich Wansing
    Pages 15-25
  4. Heinrich Wansing
    Pages 27-46
  5. Heinrich Wansing
    Pages 75-85
  6. Heinrich Wansing
    Pages 155-170
  7. Heinrich Wansing
    Pages 189-210
  8. Heinrich Wansing
    Pages 211-234
  9. Back Matter
    Pages 235-252

About this book

Introduction

The present monograph is a slightly revised version of my Habilitations­ schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.

Keywords

Cut-elimination theorem Extension logic modal logic nonmonotonic reasoning predicate logic proof semantics sequent calculus

Authors and affiliations

  • Heinrich Wansing
    • 1
  1. 1.Institute of Logic and Philosophy of ScienceUniversity of LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1280-4
  • Copyright Information Springer Science+Business Media B.V. 1998
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5079-3
  • Online ISBN 978-94-017-1280-4
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • Buy this book on publisher's site