Multiple-Conclusion Logic

This is a sustained study of the subject and is certain to stimulate further research.

D. J. Shoesmith (Author), T. J. Smiley (Author)

9780521093323, Cambridge University Press

Paperback / softback, published 11 January 2009

416 pages
22.9 x 15.2 x 2.3 cm, 0.6 kg

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.

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.

Subject Areas: Mathematical foundations [PBC]