Intermediate Logic.

By: Bostock, DavidPublisher: Oxford : Oxford University Press, Incorporated, 1997Copyright date: ©1997Description: 1 online resource (404 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9780191567070Subject(s): Logic, Symbolic and mathematical.;LogicGenre/Form: Electronic books. Additional physical formats: Print version:: Intermediate LogicDDC classification: 160 LOC classification: BC135.B473 1997Online resources: Click to View
Contents:
Intro -- CONTENTS -- Part I. SEMANTICS -- 1. Introduction -- 1.1. Truth -- 1.2. Validity -- 1.3. The Turnstile -- 2. Truth-Functors -- 2.1. Truth-Functions -- 2.2. Truth-Functors -- 2.3. Languages for Truth-Functors -- 2.4. Semantics for these Languages -- 2.5. Some Principles of Entailment -- 2.6. Normal Forms (DNF, CNF) -- 2.7. Expressive Adequacy I -- 2.8. Argument by Induction -- 2.9. Expressive Adequacy II -- 2.10. Duality -- 2.11. Truth-value Analysis -- 3. Quantifiers -- 3.1. Names and Extensionality -- 3.2. Predicates, Variables, Quantifiers -- 3.3. Languages for Quantifiers -- 3.4. Semantics for these Languages -- 3.5. Some Lemmas on these Semantics -- 3.6. Some Principles of Entailment -- 3.7. Normal Forms (PNF) -- 3.8. Decision Procedures I: One-Place Predicates -- 3.9. Decision Procedures II: ∀∃-Formulae -- 3.10. The General Situation: Proofs and Counter-examples -- Part II. PROOFS -- 4. Semantic Tableaux -- 4.1. The Idea -- 4.2. The Tableau Rules -- 4.3. A Simplified Notation -- 4.4. Constructing Proofs -- 4.5. Soundness -- 4.6. Completeness I: Truth-Functors -- 4.7. Completeness II: Quantifiers -- 4.8. Further Remarks on Completeness, Compactness, and Decidability -- 4.9. Appendix: A Direct Proof of the Cut Principle -- 5. Axiomatic Proofs -- 5.1. The Idea -- 5.2. Axioms for the Truth-Functors -- 5.3. The Deduction Theorem -- 5.4. Some Laws of Negation -- 5.5. A Completeness Proof -- 5.6. Axioms for the Quantifiers -- 5.7. Definitions of Other Logical Symbols -- 5.8. Appendix: Some Alternative Axiomatizations -- 6. Natural Deduction -- 6.1. The Idea -- 6.2. Rules of Proof I: Truth-Functors -- 6.3. Rules of Proof II: Quantifiers -- 6.4. Alternative Styles of Proof -- 6.5. Interim Review -- 7. Sequent Calculi -- 7.1. The Idea -- 7.2. Natural Deduction as a Sequent Calculus -- 7.3. Semantic Tableaux as a Sequent Calculus.
7.4. Gentzen Sequents -- Semantic Tableaux Again -- 7.5. Comparison of Systems -- 7.6. Reasoning with Gentzen Sequents -- Part III. FURTHER TOPICS -- 8. Existence and Identity -- 8.1. Identity -- 8.2. Functions -- 8.3. Descriptions -- 8.4. Empty Names and Empty Domains -- 8.5. Extensionality Reconsidered -- 8.6. Towards a Universally Free Logic -- 8.7. A Formal Presentation -- 8.8. Appendix: A Note on Names, Descriptions, and Scopes -- REFERENCES -- LIST OF SYMBOLS -- LIST OF AXIOMS AND RULES OF INFERENCE -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.
Summary: Intermediate Logic fills a serious gap in the range of university logic texts by offering a clear, reliable, general guide for students taking a second course in logic after completing a basic introduction. It will serve as an ideal follow-up to any of the standard introductory texts, and will give excellent preparation for advanced work in logical theory or applications of logic in philosophy, mathematics, or computing theory.
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Intro -- CONTENTS -- Part I. SEMANTICS -- 1. Introduction -- 1.1. Truth -- 1.2. Validity -- 1.3. The Turnstile -- 2. Truth-Functors -- 2.1. Truth-Functions -- 2.2. Truth-Functors -- 2.3. Languages for Truth-Functors -- 2.4. Semantics for these Languages -- 2.5. Some Principles of Entailment -- 2.6. Normal Forms (DNF, CNF) -- 2.7. Expressive Adequacy I -- 2.8. Argument by Induction -- 2.9. Expressive Adequacy II -- 2.10. Duality -- 2.11. Truth-value Analysis -- 3. Quantifiers -- 3.1. Names and Extensionality -- 3.2. Predicates, Variables, Quantifiers -- 3.3. Languages for Quantifiers -- 3.4. Semantics for these Languages -- 3.5. Some Lemmas on these Semantics -- 3.6. Some Principles of Entailment -- 3.7. Normal Forms (PNF) -- 3.8. Decision Procedures I: One-Place Predicates -- 3.9. Decision Procedures II: ∀∃-Formulae -- 3.10. The General Situation: Proofs and Counter-examples -- Part II. PROOFS -- 4. Semantic Tableaux -- 4.1. The Idea -- 4.2. The Tableau Rules -- 4.3. A Simplified Notation -- 4.4. Constructing Proofs -- 4.5. Soundness -- 4.6. Completeness I: Truth-Functors -- 4.7. Completeness II: Quantifiers -- 4.8. Further Remarks on Completeness, Compactness, and Decidability -- 4.9. Appendix: A Direct Proof of the Cut Principle -- 5. Axiomatic Proofs -- 5.1. The Idea -- 5.2. Axioms for the Truth-Functors -- 5.3. The Deduction Theorem -- 5.4. Some Laws of Negation -- 5.5. A Completeness Proof -- 5.6. Axioms for the Quantifiers -- 5.7. Definitions of Other Logical Symbols -- 5.8. Appendix: Some Alternative Axiomatizations -- 6. Natural Deduction -- 6.1. The Idea -- 6.2. Rules of Proof I: Truth-Functors -- 6.3. Rules of Proof II: Quantifiers -- 6.4. Alternative Styles of Proof -- 6.5. Interim Review -- 7. Sequent Calculi -- 7.1. The Idea -- 7.2. Natural Deduction as a Sequent Calculus -- 7.3. Semantic Tableaux as a Sequent Calculus.

7.4. Gentzen Sequents -- Semantic Tableaux Again -- 7.5. Comparison of Systems -- 7.6. Reasoning with Gentzen Sequents -- Part III. FURTHER TOPICS -- 8. Existence and Identity -- 8.1. Identity -- 8.2. Functions -- 8.3. Descriptions -- 8.4. Empty Names and Empty Domains -- 8.5. Extensionality Reconsidered -- 8.6. Towards a Universally Free Logic -- 8.7. A Formal Presentation -- 8.8. Appendix: A Note on Names, Descriptions, and Scopes -- REFERENCES -- LIST OF SYMBOLS -- LIST OF AXIOMS AND RULES OF INFERENCE -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.

Intermediate Logic fills a serious gap in the range of university logic texts by offering a clear, reliable, general guide for students taking a second course in logic after completing a basic introduction. It will serve as an ideal follow-up to any of the standard introductory texts, and will give excellent preparation for advanced work in logical theory or applications of logic in philosophy, mathematics, or computing theory.

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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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