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| THE MANY VALUED AND NONMONOTONIC TURN IN LOGIC, 8
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 To order this title, and for more information, click here
Edited By
Dov M. Gabbay, King's College London, UK
John Woods, University of British Columbia, Canada
Included in series
Handbook of the History of Logic,
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.
In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences
to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent
inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent,
inputs.
The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of
logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics,
computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas.
Audience
Researchers and historians in all areas of logic, including theorists, theorists of legal reasoning and cognitive psychologists
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 Redei)
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
Bibliographic & ordering Information
Hardbound, 690 pages, publication date: JUL-2007
ISBN-13: 978-0-444-51623-7
ISBN-10: 0-444-51623-9
Imprint: NORTH-HOLLAND
Price: Order form
GBP 130
USD 225
EUR 185
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Last update: 26 Aug 2008
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