Quantifiers, propositions and identity : admissible semantics for quantified modal and substructural logics / Robert Goldblatt.

Format:

Book

Author/Creator:

Goldblatt, Robert, author.

Series:

Lecture notes in logic ; 38.

Lecture notes in logic ; 38

Language:

English

Subjects (All):

Modality (Logic).

Variables (Mathematics).

Semantics (Philosophy).

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (xiii, 268 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Quantifiers, Propositions & Identity

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

Summary:

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.

Contents:

Introduction and overview

Chapter 1. Logics with actualist quantifiers

Chapter 2. The Barcan formulas

Chapter 3. The existence predicate

Chapter 4. Propositional functions and predicate substitution

Chapter 5. Identity

Chapter 6. Cover semantics for relevant logic.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-09842-X

1-139-09910-8

1-139-10178-1

1-139-09978-7

0-511-86235-0

OCLC:

923617216