Description

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity”, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity”, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.

Key Features

  • Detailed and comprehensive chapters covering the entire range of modal logic.
  • Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Readership

Researchers and historians in all areas of logic, including theorists, theorists of legal reasoning and cognitive psychologists

Table of Contents

Preface List of Contributors Chapter 1. Many-valued Logic (Grzegorz Malinowski) Chapter 2. Paraconsistent Logic: Preservationist Variations (Bryson Brown) Chapter 3. Paraconsistent Logic: Dialethic Variations (Graham Priest) Chapter 4. Quantum Logic (M. Dalla Chiara, Roberto Giuntini and Miklos Rédei) Chapter 5. Logic of Vagueness (Dominic Hyde) Chapter 6. Fuzzy Logic (Didier Dubois, Henri Prade and Lluis Godo) Chapter 7. Non-monotonic Logic (Karl Schlechta) Chapter 8. Default Logic (Grigoris Antoniou and Kewen Wang) Chapter 9. Non-monotonic Reasoning and Belief Change (Alexander Bochman) Chapter 10. Free Logic (Carl Posy) Index

Details

No. of pages:
690
Language:
English
Copyright:
© 2007
Published:
Imprint:
North Holland
Electronic ISBN:
9780080549392
Print ISBN:
9780444516237

About the editors

Dov M. Gabbay

Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.