Multiple-Conclusion Logic

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Paperback | 11 January 2009

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416 Pages

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22.86 x 15.24 x 2.36

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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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You Can Find This Book In

Non-Fiction Philosophy Philosophy & Logic Mathematics Mathematical Foundation Mathematical Logic Earth Sciences, Geography, Environment, Planning Earth Sciences Geology & The Lithosphere

Preface
Introduction
Multiple and Single Conclusions
Single-conclusion calculi
Multiple-conclusion calculi
Tree proofs
Axiomatisability
Counterparts
Infinite rules
Graph Proofs
Graph arguments
Kneale proofs
Cross-reference
Abstract proofs
Single-conclusions proofs
Infinite proofs
Many-valued Logic
Many-valued calculi
matrices
Many-valuedness
Counterparts
Categoricity
Two-valued logic
Axiomatisation
Natural Deduction
Natural Deduction
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Multiple-Conclusion Logic

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Paperback

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