"Intermediate Logic" is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding. The author introduces and explains each concept and term, ensuring readers have a firm foundation for study. He provides a broad, deep understanding of logic by adopting and comparing a variety of different methods and approaches
Author(s): David Bostock
Publisher: Oxford University Press
Year: 1997
Language: English
Commentary: OCR, Front and Back Covers, Bookmarks, Pagination
Pages: 408
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 ldea
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
