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Quantifiers, Propositions and Identity Admissible Semantics for Quantified Modal and Substructural Logics by Robert (Victoria University of Wellington) Goldblatt
  

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

Part of the Lecture Notes in Logic Series

RRP £60.00

Synopsis

Quantifiers, Propositions and Identity Admissible Semantics for Quantified Modal and Substructural Logics by Robert (Victoria University of Wellington) Goldblatt

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.

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Book Info

Publication date

14th July 2011

Author

Robert (Victoria University of Wellington) Goldblatt

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Publisher

Cambridge University Press

Format

Hardback
282 pages

Categories

Mathematical logic

ISBN

9781107010529

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