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  3. Multiple-Conclusion Logic
  • Cited by 201
Publisher:
Cambridge University Press
Online publication date:
July 2010
Print publication year:
1978
Online ISBN:
9780511565687
DOI:
https://doi.org/10.1017/CBO9780511565687
Subjects:
Mathematics, Logic, Categories and Sets, Philosophy of Science, Philosophy
Information

Book description

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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