QUANTIFIERS, PROPOSITIONS AND IDENTITY by Robert Goldblatt ( 9781107010529 )

Item Details

Title:

QUANTIFIERS, PROPOSITIONS AND IDENTITY
ADMISSIBLE SEMANTICS FOR QUANTIFIED MODAL AND SUBSTRUCTURAL LOGICS

By:

Robert Goldblatt

Format:

Hardback

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£111.00

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£99.90

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£11.10

ISBN 10:

1107010527

ISBN 13:

9781107010529

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

14 July, 2011

Series:

Lecture Notes in Logic 38

Pages:

282

Description:

Develops new semantical characterisations of many logical systems with quantification that are incomplete under the traditional Kripkean possible worlds interpretation.

Synopsis:

Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of quantification. The theory is worked out for systems with quantifiers ranging over actual objects, and over all possibilia, and for logics with existence and identity predicates and definite descriptions. The final chapter develops a new admissible 'cover semantics' for propositional and quantified relevant logic, adapting ideas from the Kripke-Joyal semantics for intuitionistic logic in topos theory. This book is for mathematical or philosophical logicians, computer scientists and linguists.

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Imprint:

Cambridge University Press

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Returnable

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