The Many Valued and Nonmonotonic Turn in Logic, Vol 8. Handbook of the History of Logic

  • ID: 1764620
  • July 2007
  • 690 Pages
  • Elsevier Science and Technology
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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 READ MORE >

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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)

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Gabbay, Dov M.
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.
Woods, John

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