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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. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. Many-valued logics produce an interesting problem. 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, 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 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. These are many-valuedness and non-monotonicity.
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. It is a very powerful and stable OS X release.
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