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

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

Robert Goldblatt (Author)

9781107010529, Cambridge University Press

Hardback, published 14 July 2011

282 pages
23.5 x 16 x 1.9 cm, 0.52 kg

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.

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.

Subject Areas: Mathematical logic [PBCD]