Quantifiers, Propositions and Identity
Admissible Semantics for Quantified Modal and Substructural Logics
Published on 11. May 2012
282 pages
978-1-139-09842-7 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
2253,89 MB
ISBN-13
978-1-139-09842-7 (9781139098427)
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Schweitzer Classification
Other editions
Additional editions
Robert Goldblatt
Quantifiers, Propositions and Identity
Admissible Semantics for Quantified Modal and Substructural Logics
Book
07/2011
Cambridge University Press
€154.00
Shipment within 15-20 days
Person
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.
Content
Introduction and overview; 1. Logics with actualist quantifiers; 2. The Barcan formulas; 3. The existence predicate; 4. Propositional functions and predicate substitution; 5. Identity; 6. Cover semantics for relevant logic; References; Index.
