Multiple-conclusion logic extends formal logic by allowing
arguments to have a set of conclusions instead of a single one, the
truth lying somewhere among the conclusions if all the premises are
true. The extension opens up interesting possibilities based on the
symmetry between premises and conclusions, and can also be used to
throw fresh light on the conventional logic and its limitations.
This is a sustained study of the subject and is certain to
stimulate further research. Part I reworks the fundamental ideas of
logic to take account of multiple conclusions, and investigates the
connections between multiple - and single - conclusion calculi.
Part II draws on graph theory to discuss the form and validity of
arguments independently of particular logical systems. Part III
contrasts the multiple - and the single - conclusion treatment of
one and the same subject, using many-valued logic as the example;
and Part IV shows how the methods of 'natural deduction' can be
matched by direct proofs using multiple conclusions.
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