Description

Book Synopsis

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.

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.

MultipleConclusion Logic

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

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      Book details

      Publisher Cambridge University Press
      Published 11 January 2009
      ISBN-13 9780521093323
      978-0521093323
      ISBN-10 0521093325
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      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.

      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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