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

By: Goldblatt, RobertSeries: 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 resourceISBN: 9781139099783Subject(s): Modality (Logic);Variables (Mathematics);Semantics (Philosophy);Logic, Symbolic and mathematicalGenre/Form: Electronic books. 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 2011Online resources: Click to View
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.

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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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