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A New Perspective on Nonmonotonic Logics

  • Dov M. Gabbay
  • Karl Schlechta
Book
  • 4.6k Downloads

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Dov M. Gabbay, Karl Schlechta
      Pages 3-62
  3. Background Material

    1. Front Matter
      Pages 63-63
    2. Dov M. Gabbay, Karl Schlechta
      Pages 65-74
    3. Dov M. Gabbay, Karl Schlechta
      Pages 75-90
    4. Dov M. Gabbay, Karl Schlechta
      Pages 91-95
    5. Dov M. Gabbay, Karl Schlechta
      Pages 97-130
    6. Dov M. Gabbay, Karl Schlechta
      Pages 131-144
    7. Dov M. Gabbay, Karl Schlechta
      Pages 145-157
    8. Dov M. Gabbay, Karl Schlechta
      Pages 159-174
  4. New Results

    1. Front Matter
      Pages 175-175
    2. Dov M. Gabbay, Karl Schlechta
      Pages 177-199
    3. Dov M. Gabbay, Karl Schlechta
      Pages 201-232
    4. Dov M. Gabbay, Karl Schlechta
      Pages 233-266
    5. Dov M. Gabbay, Karl Schlechta
      Pages 267-282
    6. Dov M. Gabbay, Karl Schlechta
      Pages 283-344
    7. Dov M. Gabbay, Karl Schlechta
      Pages 345-349
  5. Back Matter
    Pages 351-365

About this book

Introduction

"Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its value for classical and other forms of deductive inference; this book manifests its pertinence to logics of uncertain qualitative reasoning. It draws together and refines work from the literature on preferential and other quite different semantics for such reasoning and then, in its central chapter, integrates the leading ideas from them into a single multi-dimensional semantics. It enters new territory with investigations of interpolation and qualitative independence in non-monotonic contexts as well as connections between non-monotonic logic and neuroscience, specifically with Edelman’s theory of organization of the brain. Finally, it proposes novel applications such as equational modellings for contrary-to-duty normative reasoning and mathematical analyses of some kinds of casuistic reasoning in the Talmudic tradition. Profusely signposted at every turn, the volume is accessible to readers equipped with a modicum of set theory and abstract algebra. Visitors to the area can come in by the front gate and work their way, in various orders, through as much of the garden as strikes their fancy; specialists will enter at Chap. 11 or at whatever special topic interests them, well assured that they can easily backtrack to whatever bits and pieces are needed from what they skipped. A volume with a clear vision, a book to return to many times."  (David Makinson)

Keywords

Logic Mathematical Logic Meta-rules Nonmonotonic Logic (NML) Philosophy of Science Rarity Defeasible Inheritance Deontic Logic Theory Revision Counterfactuals Neurology

Authors and affiliations

  • Dov M. Gabbay
    • 1
  • Karl Schlechta
    • 2
  1. 1.King's College London, Bar-Ilan University, Université de LuxembourgLondonUnited Kingdom
  2. 2.CNRS, LIF UMR 7279Aix-Marseille UniversitéMarseilleFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-46817-4
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-46815-0
  • Online ISBN 978-3-319-46817-4
  • Buy this book on publisher's site