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Labelled Non-Classical Logics

  • Luca Viganò

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Luca Viganò
      Pages 1-14
  3. Labelled deduction for non-classical logics

  4. Substructural and complexity analysis of modal sequent systems

    1. Front Matter
      Pages 165-165
    2. Luca Viganò
      Pages 167-185
    3. Luca Viganò
      Pages 187-200
    4. Luca Viganò
      Pages 201-222
    5. Luca Viganò
      Pages 223-246
    6. Luca Viganò
      Pages 253-262
    7. Luca Viganò
      Pages 263-265
  5. Back Matter
    Pages 267-291

About this book

Introduction

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.

Keywords

calculus complexity modal logic proof proof theory

Authors and affiliations

  • Luca Viganò
    • 1
  1. 1.Institut für InformatikAlbert-Ludwigs-Universität FreiburgFreiburg im BreisgauGermany

Bibliographic information