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

By: Series: Lecture Notes in LogicPublisher: Cambridge : Cambridge University Press, 2011Copyright date: ©2011Description: 1 online resource (284 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781139099783
Subject(s): Genre/Form: Additional physical formats: Print version:: Quantifiers, Propositions and Identity : Admissible Semantics for Quantified Modal and Substructural LogicsDDC classification:
  • 511.3
LOC classification:
  • QA9.46 .G664 2011
Online resources:
Contents:
Cover -- Title -- Copyright -- Contents -- Introduction and Overview -- Chapter 1. Logics with Actualist Quantifiers -- 1.1. Syntax -- 1.2. Logics -- 1.3. Incompleteness and Admissibility -- 1.4. Some History of the Quantifiers. -- 1.5. Model Structures -- 1.6. Premodels and Models -- 1.7. Soundness -- 1.8. Infinitely Many Constants -- 1.9. Canonical Models and Completeness -- 1.10. Completeness and Canonicity for QS -- 1.11. Kinds of Incompleteness -- 1.11.1. Incompleteness for Kripkean Models -- 1.11.2. Kripkean S-frame Incompleteness -- 1.11.3. Non-Canonical S-frame Incompleteness -- Chapter 2. The Barcan Formulas -- 2.1. Logics with CBF -- 2.2. Contracting Domains for All -- 2.3. Constant Domains for CBF -- 2.4. One Universal Domain -- 2.5. The Deductive Role of Commuting Quantifiers -- 2.6. Completeness with CBF and BF -- 2.7. Completeness with UI and BF. -- 2.8. S-frame Incompleteness Revisited -- Chapter 3. The Existence Predicate -- 3.1. Axiomatising Existence -- 3.2. Completeness for Kripkean E-Models -- 3.3. Necessity of (Non)Existence -- 3.4. Independence of BF from NNE -- 3.5. What is the Role of the Barcan Formula? -- Chapter 4. Propositional Functions and Predicate Substitution -- 4.1. Functional Model Structures -- 4.2. Predicate Substitution: Notation and Terminology -- 4.3. The Anatomy of Predicate Substitution -- 4.3.1. Changing Bound Variables -- 4.3.2. Sufficient Freeness -- 4.3.3. Defining φ(ΨP/PxP : P ∈ Π) in General -- 4.3.4. Strongly Free Substitution -- 4.3.5. Parameterless Substitution -- 4.4. Soundness of Predicate Substitution -- 4.5. Functional Canonicity -- Chapter 5. Identity -- 5.1. Intension versus Extension -- 5.2. Syntax -- 5.3. Identity and Rigid Functions -- 5.4. Model Structures and Models -- 5.5. Validity of Substitutivity of Identicals -- 5.6. Axiomatisation and Completeness -- 5.7. Kripkean Models.
5.8. Definite Descriptions -- Chapter 6. Cover Semantics for Relevant Logic -- 6.1. Routley-Meyer Models for R -- 6.2. Admissible Semantics for RQ -- 6.3. Local Truth and Covers -- 6.4. Relevant Cover Systems -- 6.5. Cover System Completeness for R -- 6.6. Modelling Fusion -- 6.7. Cover System Characterisation of RQ -- 6.8. Heyting Implication for Full Systems -- 6.9. Localic Cover Systems for HR and HRQ -- References -- Index.
Summary: Develops new semantical characterisations of many logical systems with quantification that are incomplete under the traditional Kripkean possible worlds interpretation.
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Cover -- Title -- Copyright -- Contents -- Introduction and Overview -- Chapter 1. Logics with Actualist Quantifiers -- 1.1. Syntax -- 1.2. Logics -- 1.3. Incompleteness and Admissibility -- 1.4. Some History of the Quantifiers. -- 1.5. Model Structures -- 1.6. Premodels and Models -- 1.7. Soundness -- 1.8. Infinitely Many Constants -- 1.9. Canonical Models and Completeness -- 1.10. Completeness and Canonicity for QS -- 1.11. Kinds of Incompleteness -- 1.11.1. Incompleteness for Kripkean Models -- 1.11.2. Kripkean S-frame Incompleteness -- 1.11.3. Non-Canonical S-frame Incompleteness -- Chapter 2. The Barcan Formulas -- 2.1. Logics with CBF -- 2.2. Contracting Domains for All -- 2.3. Constant Domains for CBF -- 2.4. One Universal Domain -- 2.5. The Deductive Role of Commuting Quantifiers -- 2.6. Completeness with CBF and BF -- 2.7. Completeness with UI and BF. -- 2.8. S-frame Incompleteness Revisited -- Chapter 3. The Existence Predicate -- 3.1. Axiomatising Existence -- 3.2. Completeness for Kripkean E-Models -- 3.3. Necessity of (Non)Existence -- 3.4. Independence of BF from NNE -- 3.5. What is the Role of the Barcan Formula? -- Chapter 4. Propositional Functions and Predicate Substitution -- 4.1. Functional Model Structures -- 4.2. Predicate Substitution: Notation and Terminology -- 4.3. The Anatomy of Predicate Substitution -- 4.3.1. Changing Bound Variables -- 4.3.2. Sufficient Freeness -- 4.3.3. Defining φ(ΨP/PxP : P ∈ Π) in General -- 4.3.4. Strongly Free Substitution -- 4.3.5. Parameterless Substitution -- 4.4. Soundness of Predicate Substitution -- 4.5. Functional Canonicity -- Chapter 5. Identity -- 5.1. Intension versus Extension -- 5.2. Syntax -- 5.3. Identity and Rigid Functions -- 5.4. Model Structures and Models -- 5.5. Validity of Substitutivity of Identicals -- 5.6. Axiomatisation and Completeness -- 5.7. Kripkean Models.

5.8. Definite Descriptions -- Chapter 6. Cover Semantics for Relevant Logic -- 6.1. Routley-Meyer Models for R -- 6.2. Admissible Semantics for RQ -- 6.3. Local Truth and Covers -- 6.4. Relevant Cover Systems -- 6.5. Cover System Completeness for R -- 6.6. Modelling Fusion -- 6.7. Cover System Characterisation of RQ -- 6.8. Heyting Implication for Full Systems -- 6.9. Localic Cover Systems for HR and HRQ -- References -- Index.

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

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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