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Multiple-Conclusion Logic

$65.00

  • Date Published: January 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521093323

$65.00
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  • 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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    Product details

    • Date Published: January 2009
    • format: Paperback
    • isbn: 9780521093323
    • length: 416 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.61kg
    • availability: Available
  • 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.

  • Authors

    D. J. Shoesmith
    fm.author_biographical_note1

    T. J. Smiley
    fm.author_biographical_note2

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