Admissibility of Logical Inference Rules

by Rybakov

• ISBN13: 9780444895059
• ISBN10: 0444895051
• Format: Hardcover
• Copyright: 1997-03-14
• Publisher: Elsevier Science

Summary

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on:bull; admissible or permissible inference rulesbull; the derivability of the admissible inference rulesbull; the structural completeness of logicsbull; the bases for admissible and valid inference rules.There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered.The book is basically self-contained and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included.The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook.

Table of Contents

Preface and Acknowledgments	p. 3
Introduction	p. 8
Syntaxes and Semantics	p. 17
Semantics for Non-Standard Logics	p. 103
Criteria for Admissibility	p. 279
Bases for Inference Rules	p. 393
Structural Completeness	p. 475
Related Questions	p. 525
Index	p. 595
Bibliography	p. 603
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