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
Year: 1997
Language: English
Pages: 404
0198751419......Page 1
CONTENTS......Page 8
Part I. SEMANTICS......Page 12
1.1. Truth......Page 14
1.2. Validity......Page 16
1.3. The Turnstile......Page 19
2.1. Truth-Functions......Page 25
2.2. Truth-Functors......Page 28
2.3. Languages for Truth-Functors......Page 32
2.4. Semantics for these Languages......Page 35
2.5. Some Principles of Entailment......Page 41
2.6. Normal Forms (DNF, CNF)......Page 48
2.7. Expressive Adequacy I......Page 56
2.8. Argument by Induction......Page 59
2.9. Expressive Adequacy II......Page 67
2.10. Duality......Page 73
2.11. Truth-value Analysis......Page 76
3.1. Names and Extensionality......Page 81
3.2. Predicates, Variables, Quantifiers......Page 85
3.3. Languages for Quantifiers......Page 88
3.4. Semantics for these Languages......Page 92
3.5. Some Lemmas on these Semantics......Page 102
3.6. Some Principles of Entailment......Page 107
3.7. Normal Forms (PNF)......Page 120
3.8. Decision Procedures I: One-Place Predicates......Page 126
3.9. Decision Procedures II: ∀∃-Formulae......Page 137
3.10. The General Situation: Proofs and Counter-examples......Page 142
Part II. PROOFS......Page 150
4.1. The Idea......Page 152
4.2. The Tableau Rules......Page 158
4.3. A Simplified Notation......Page 163
4.4. Constructing Proofs......Page 168
4.5. Soundness......Page 176
4.6. Completeness I: Truth-Functors......Page 179
4.7. Completeness II: Quantifiers......Page 185
4.8. Further Remarks on Completeness, Compactness, and Decidability......Page 193
4.9. Appendix: A Direct Proof of the Cut Principle......Page 198
5.1. The Idea......Page 201
5.2. Axioms for the Truth-Functors......Page 204
5.3. The Deduction Theorem......Page 211
5.4. Some Laws of Negation......Page 219
5.5. A Completeness Proof......Page 228
5.6. Axioms for the Quantifiers......Page 231
5.7. Definitions of Other Logical Symbols......Page 238
5.8. Appendix: Some Alternative Axiomatizations......Page 243
6.1. The Idea......Page 250
6.2. Rules of Proof I: Truth-Functors......Page 253
6.3. Rules of Proof II: Quantifiers......Page 265
6.4. Alternative Styles of Proof......Page 273
6.5. Interim Review......Page 280
7.1. The Idea......Page 284
7.2. Natural Deduction as a Sequent Calculus......Page 288
7.3. Semantic Tableaux as a Sequent Calculus......Page 294
7.4. Gentzen Sequents; Semantic Tableaux Again......Page 302
7.5. Comparison of Systems......Page 310
7.6. Reasoning with Gentzen Sequents......Page 318
Part III. FURTHER TOPICS......Page 332
8.1. Identity......Page 334
8.2. Functions......Page 344
8.3. Descriptions......Page 352
8.4. Empty Names and Empty Domains......Page 359
8.5. Extensionality Reconsidered......Page 366
8.6. Towards a Universally Free Logic......Page 371
8.7. A Formal Presentation......Page 377
8.8. Appendix: A Note on Names, Descriptions, and Scopes......Page 386
REFERENCES......Page 390
LIST OF SYMBOLS......Page 394
LIST OF AXIOMS AND RULES OF INFERENCE......Page 396
E......Page 402
O......Page 403
W......Page 404
