Multiple-Conclusion Logic

Multiple-Conclusion Logic

by D. J. Shoesmith, T. J. Smiley
     
 

ISBN-10: 0521093325

ISBN-13: 9780521093323

Pub. Date: 01/11/2009

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521093323
Publisher:
Cambridge University Press
Publication date:
01/11/2009
Pages:
416
Product dimensions:
6.00(w) x 9.00(h) x 1.10(d)

Table of Contents

Preface; Introduction; Part I. Multiple and Single Conclusions; 1. Single-conclusion calculi; 2. Multiple-conclusion calculi; 3. Tree proofs; 4. Axiomatisability; 5. Counterparts; 6. Infinite rules; Part II. Graph Proofs; 7. Graph arguments; 8. Kneale proofs; 9. Cross-reference; 10. Abstract proofs; 11. Single-conclusions proofs; 12. Infinite proofs; Part III: Many-valued Logic; 13. Many-valued calculi; 14. matrices; 15. Many-valuedness; 16. Counterparts; 17. Categoricity; 18. Two-valued logic; 19. Axiomatisation; Part IV. Natural Deduction; 20. Natural Deduction; Bibliography; Index.

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