Quantifiers, propositions, and identity
Subtitle: admissible semantics for quantified modal and substructural logics
By: Robert Goldblatt
Series: Lecture notes in logic -- 38
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge; New York
Language: eng
Number of pages: 282
ISBN-13: 9781107010529
Subjects: MATHEMATICS / Logic; Modality (Logic); Symbolic and mathematical Logic; Semantics (Philosophy); Variables (Mathematics)
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"--
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: 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.