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An Essay on Contraction cover

An Essay on Contraction

André Fuhrmann

This book generalizes earlier theories of belief change to cover all kinds of changes of sets by sets. The principal focus is still on changes of belief sets in response to new evidence. But the formal theory extends to all domains with a closure operation and a preference structure, including, for example, systems of action. Contraction is the key notion; all other changes can be defined. Various new applications of the theory are outlined. A sentential version of contractio, subtraction, is proposed as a formal conterpart to “except”-locutions in natural language. Connections are emphasized with other areas at the interface between philosophical logic and artificial intelligence such as reasoning from default assumptions or from inconsistent premisses. A relation of merge inference is proposed as a means of retrieving maximal but nontrivial information from inconsistent premisses. Merge inference respects certain anti-Boolean intuitions while avoiding a revision of classical logic.

André Fuhrmann is a lecturer in Philosophy at the University of Konstanz.


  • Preface
  • 1 Introduction
  • 2 Theories and Theory Change
    • 2.1 Sentential Languages and Consequence Operations
    • 2.2 Three Kinds of Theory Change
    • 2.3 The AGM Postulates
    • 2.4 Construcitons
  • 3 General Contraction
    • 3.1 An Imbalance
    • 3.2 Closure
    • 3.3 Very Small Changes
    • 3.4 Do, Need, and Should We Multiply Contract?
    • 3.5 Package Contractionand Choice Contraction
    • 3.6 Basic Properties of Multiple Contraction
    • 3.7 Tools for Constructing General Contraction Functions
    • 3.8 Constructing Contractions
    • 3.9 Reduction Strategies Revisited
    • 3.10 Theory Contraction through Base Replacements
    • 3.11 Why General Contraction is General Enough
    • 3.12 Logical Subtraction Revisited
  • 4 Revision, Merge and Inference
    • 4.1 Revision
    • 4.2 Merge
    • 4.3 Inference
  • 5 Everything in Flux: Dynamic Ontologies
    • 5.1 Closure Systems and Ontological Spaces
    • 5.2 Travelling in Ontological Space
    • 5.3 Finding (Good) Examples
  • Bibliography
  • Notation
  • Name Index
  • Subject Index


ISBN (Paperback): 1575860546 (9781575860541)
ISBN (Cloth): 1575860554 (9781575860558)
ISBN (Electronic): 1575867966 (9781575867960)
Subject: Philosophy; Belief and Doubt; Logic

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