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Labelled Non-Classical Logics

  • Book
  • © 2000

Overview

Authors:
  1. Luca Viganò

    1. Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    1. Introduction

      • Luca Viganò
      Pages 1-14

  3. Labelled deduction for non-classical logics

    1. Front Matter

      Pages 15-15
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    2. Labelled Natural Deduction Systems for Propositional Modal Logics

      • Luca Viganò
      Pages 17-52

    3. Labelled Natural Deduction Systems for Propositional Non-Classical Logics

      • Luca Viganò
      Pages 53-89

    4. Labelled Natural Deduction Systems for Quantified Modal Logics

      • Luca Viganò
      Pages 91-113

    5. Encoding Labelled Non-Classical Logics in Isabelle

      • Luca Viganò
      Pages 115-135

    6. Labelled Sequent Systems for Non-Classical Logics

      • Luca Viganò
      Pages 137-156

    7. Discussion

      • Luca Viganò
      Pages 157-164

  4. Substructural and complexity analysis of modal sequent systems

    1. Front Matter

      Pages 165-165
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    2. Introduction and Preliminaries

      • Luca Viganò
      Pages 167-185

    3. Substructural Analysis of S(K)

      • Luca Viganò
      Pages 187-200

    4. Substructural Analysis of S(T)

      • Luca Viganò
      Pages 201-222

    5. Substructural Analysis of S(K4) and S(S4)

      • Luca Viganò
      Pages 223-246

    6. Complexity of Proof Search in K, T, K4 and S4

      • Luca Viganò
      Pages 247-252

    7. Discussion

      • Luca Viganò
      Pages 253-262

    8. Conclusions and Further Research

      • Luca Viganò
      Pages 263-265

  5. Back Matter

    Pages 267-291
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Keywords

About this book

I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof­ theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys­ tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.

Authors and Affiliations

  • Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany

    Luca Viganò

About the author

Luca Viganò is an assistant professor at the Institute for Computer Science of the University of Freiburg (Germany). His research focuses on the theory and applications of non-classical logics, of proof development systems, of logical frameworks, and of logics for security.

Bibliographic Information

  • Book Title: Labelled Non-Classical Logics

  • Authors: Luca Viganò

  • DOI: https://doi.org/10.1007/978-1-4757-3208-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2000

  • Hardcover ISBN: 978-0-7923-7749-8Published: 31 January 2000

  • Softcover ISBN: 978-1-4419-4962-2Published: 03 December 2010

  • eBook ISBN: 978-1-4757-3208-5Published: 17 April 2013

  • Edition Number: 1

  • Number of Pages: XIV, 292

  • Topics: Logic, Computer Science, general, Mathematical Logic and Foundations

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