Labelled Deductive Systems: Volume 1

Hardcover | April 30, 1999

byDov M. Gabbay

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This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas by the notion of structured families of labelled formulas, the labels having algebraic structure. This simple device has far reaching consequences forthe methodology of logics and their semantics. The book studies the main features of such systems as well as many applications.The framework of Labelled Deductive Systems is of interest to a large variety of readers. At one extreme there is the pure mathematical logician who likes exact formal definitions and dry theorems, who probably specializes in one logic and methodology. At the other extreme there is the practicalconsumer of logic, who likes to absorb the intutions and use labelling as needed to advance the cause of applications.The book begins with an intuitive presentation of LDS in the context of traditional current views of monotonic and nonmonotonic logics. It is less orientated towards the pure logician and more towards the practical consumer of logic.The main part of the book presents the formal theory of LDS for the formal logician. The author has tried to avoid the style of definition-lemma-theorem and has put in some explanation.

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This important book provides a new unifying methodology for logic. It replaces the traditional view of logic as manipulating sets of formulas by the notion of structured families of labelled formulas, the labels having algebraic structure. This simple device has far reaching consequences forthe methodology of logics and their semanti...

Dov M. Gabbay is at Imperial College, London.

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Format:HardcoverDimensions:510 pages, 9.21 × 6.14 × 1.26 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198538332

ISBN - 13:9780198538332

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Table of Contents

1. What is a logical system?2. Introducing Labelled Deductive Systems3. Algebraic LDS4. General LDS5. Resource logics6. Translation of LDS7. LDS formulation8. Curry-Howard interpretation9. Structured consequence relations10. Labelled analytic deduction11. Abduction in Labelled Deductive Systems

Editorial Reviews

`The wole exposition has been permeated wiht instructive, interesting and witty examples. The book opens a number of new interesting model-theoretic, proof-theoretic and foundational questions and seems to be a reasonable basis for new further investigations. ...Undoubtedly, this will be onof the inspiring sources motivating others to work in those fields.'B. Boricic, Zentrallblatt fur Mathematik und ihre Grenzgebiete No. 858, 1997