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ON THREE-VALUED PRESENTATIONS OF CLASSICAL LOGIC
- Part of
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- Journal:
- The Review of Symbolic Logic / Volume 17 / Issue 3 / September 2024
- Published online by Cambridge University Press:
- 11 May 2023, pp. 682-704
- Print publication:
- September 2024
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- Article
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Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations
$st$, 
$ss$, 
$tt$, 
$ss\cap tt$, and 
$ts$, when the connectives are negation, conjunction, and disjunction. For 
$ts$ and 
$ss\cap tt$ the answer is trivial (no scheme works), and for 
$ss$ and 
$tt$ it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For 
$st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.
