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

Quantifiers, Propositions and Identity Admissible Semantics for Quantified Modal and Substructural Logics by Robert Goldblatt, published by Cambridge University Press on July 14, 2011, spans 268 pages and is presented in English. This work explores the limitations of traditional systems of quantified modal logic, particularly those that cannot be adequately described by Kripke’s possible worlds semantic analysis. Goldblatt introduces a more general framework known as ‘admissible semantics,’ which reinterprets quantifiers in the context of the admissibility of propositions, providing a fresh perspective on the Barcan Formula and its implications for quantification.

Readers will find a detailed examination of various systems that incorporate quantifiers over actual objects and all possible entities, as well as logics that include existence and identity predicates. The final chapter presents an innovative ‘cover semantics’ for propositional and quantified relevant logic, drawing on concepts from Kripke-Joyal semantics within topos theory. This book is aimed at mathematical or philosophical logicians, computer scientists, and linguists, offering insights into the intersection of logic and semantics.