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Quantifiers, Propositions and Identity

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


Part of Lecture Notes in Logic

  • Date Published: July 2011
  • availability: Available
  • format: Hardback
  • isbn: 9781107010529

$ 124.95

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About the Authors
  • 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.

    • Carefully written with attention to motivation, this book is accessible to advanced students as well as researchers
    • Provides clear explanation of the background as well as new ideas
    • Introduces a new theory of 'admissible semantics' for logical systems with quantifiers
    • The author's new theory of 'cover semantics' is an attractive alternative to existing semantical theories
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    Product details

    • Date Published: July 2011
    • format: Hardback
    • isbn: 9781107010529
    • length: 282 pages
    • dimensions: 235 x 160 x 19 mm
    • weight: 0.52kg
    • availability: Available
  • Table of Contents

    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

  • Author

    Robert Goldblatt, Victoria University of Wellington
    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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