Quantifiers, Propositions and Identity Admissible Semantics for Quantified Modal and Substructural Logics

Goldblatt, Robert

ISBN 10: 1107010527 / ISBN 13: 9781107010529

Published by Cambridge University Press, 2011

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Bibliographic Details

• Title: Quantifiers, Propositions and Identity Admissible Semantics for Quantified Modal and Substructural Logics
• Publisher: Cambridge University Press
• Publication Date: 2011
• Language: English
• ISBN 10: 1107010527
• ISBN 13: 9781107010529
• Binding: Hardcover
• Condition: New

About this title

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.

About the Author

Robert Goldblatt is a Professor of Pure Mathematics at the Victoria University of Wellington, New Zealand, and a Fellow of the Royal Society of New Zealand. He has served as the Co-ordinating Editor of the Journal of Symbol Logic and has been a Managing Editor of Studia Logica for the past two decades.