ISBN-10:
0198751427
ISBN-13:
9780198751427
Pub. Date:
10/09/1997
Publisher:
Oxford University Press, USA
Intermediate Logic / Edition 1

Intermediate Logic / Edition 1

by David Bostock
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Overview

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

Product Details

ISBN-13: 9780198751427
Publisher: Oxford University Press, USA
Publication date: 10/09/1997
Edition description: New Edition
Pages: 408
Product dimensions: 6.10(w) x 9.10(h) x 1.10(d)
Lexile: 1320L (what's this?)

Table of Contents

Part I. SEMANTICS 1(138)
1. Introduction
3(11)
1.1. Truth
3(2)
1.2. Validity
5(3)
1.3. The Turnstile
8(6)
2. Truth-Functors
14(56)
2.1. Truth-Functions
14(3)
2.2. Truth-Functors
17(4)
2.3. Language for Truth-Functors
21(3)
2.4. Semantics for these Languages
24(6)
2.5. Some Principles of Entailment
30(7)
2.6. Normal Forms (DNF, CNF)
37(8)
2.7. Expressive Adequacy I
45(3)
2.8. Argument by Induction
48(8)
2.9. Expressive Adequacy II
56(6)
2.10. Duality
62(3)
2.11. Truth-value Analysis
65(5)
3. Quantifiers
70(69)
3.1. Names and Extensionality
70(4)
3.2. Predicates, Variables, Quantifiers
74(3)
3.3. Languages for Quantifiers
77(4)
3.4. Semantics for these Languages
81(10)
3.5. Some Lemmas on these Semantics
91(5)
3.6. Some Principles of Entailment
96(13)
3.7. Normal Forms (PNF)
109(6)
3.8. Decision Procedures I: One Place Predicates
115(11)
3.9. Decision Procedures II: XXX-Formulae
126(5)
3.10. The General Situation: Proofs and Counter-examples
131(8)
Part II. PROOFS 139(182)
4. Semantic Tableaux
141(49)
4.1. The Idea
141(6)
4.2. The Tableau Rules
147(5)
4.3. A Simplified Notation
152(5)
4.4. Constructing Proofs
157(8)
4.5. Soundness
165(3)
4.6. Completeness I: Truth-Functors
168(6)
4.7. Completeness II: Quantifiers
174(8)
4.8. Further Remarks on Completeness, Compactness, and Decidability
182(5)
4.9. Appendix: A Direct Proof of the Cut Principle
187(3)
5. Axiomatic Proofs
190(49)
5.1. The Idea
190(3)
5.2. Axioms for the Truth-Functors
193(7)
5.3. The Deduction Theorem
200(8)
5.4. Some Laws of Negation
208(9)
5.5. A Completeness Proof
217(3)
5.6. Axioms for the Quantifiers
220(7)
5.7. Definitions of Other Logical Symbols
227(5)
5.8. Appendix: Some Alternative Axiomatizations
232(7)
6. Natural Deduction
239(34)
6.1. The Idea
239(3)
6.2. Rules of Proof I: Truth-Functors
242(12)
6.3. Rules of Proof II: Quantifiers
254(8)
6.4. Alternative Styles of Proof
262(7)
6.5. Interim Review
269(4)
7. Sequent Calculi
273(48)
7.1. The Idea
273(4)
7.2. Natural Deduction as a Sequent Calculus
277(6)
7.3. Semantic Tableaux as a Sequent Calculus
283(8)
7.4. Gentzen Sequents; Semantic Tableaux Again
291(8)
7.5. Comparison of Systems
299(8)
7.6. Reasoning with Gentzen Sequents
307(14)
Part III. FURTHER TOPICS 321(58)
8. Existence and Identity
323(56)
8.1. Identity
323(10)
8.2. Functions
333(8)
8.3. Descriptions
341(7)
8.4. Empty Names and Empty Domains
348(7)
8.5. Extensionality Reconsidered
355(5)
8.6. Towards a Universally Free Logic
360(6)
8.7. A Formal Presentation
366(9)
8.8. Appendix: A Note on Names, Descriptions, and Scopes
375(4)
REFERENCES 379(4)
LIST OF SYMBOLS
383(1)
LIST OF AXIOMS AND RULES OF INFERENCE 384(3)
INDEX 387

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