ProofWiki:Books/Donald Kalish/Logic: Techniques of Formal Reasoning

Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning

Published 1964, Harcourt Brace Jovanovich, Inc..

ISBN 0-15-551180-7

Subject Matter

• Logic

Contents

Preface

Chapter I. 'NOT' and 'IF'

1. Symbols and sentences / Exercises

2. From symbols to English and back / Exercises

3. Derivability and validity / Exercises, Group I, Exercises, Group II

4. *Fallacies

5. Theorems / Exercises

6. *Historical remarks

Chapter II. 'AND', 'OR', 'IF AND ONLY IF'

1. Symbols and sentences / Exercises

2. Translation and symbolization / Exercises

3. Inference rules; theorems with unabbreviated proofs / Exercises

4. Abbreviated derivations / Exercises

5. Theorems with abbreviated proofs / Exercises, Group I, Exercises, Group II, Exercises, Group III

6. *Truth-value analysis of sentences / Exercises

7. *Truth-value analysis of arguments / Exercises

8. *Historical remarks

9. Appendix: list of theorems of chapters I and II

Chapter III. 'ALL' and 'SOME'

1. Variables, quantifiers, formulas / Exercises

2. Bondage and freedom / Exercises

3. Informal notational conventions

4. Translation and symbolization / Exercises

5. Inference rules and forms of derivation; theorems with unabbreviated proofs / Exercises

6. Abbreviated derivations; theorems with abbreviated proofs / Exercises

7. Arguments / Exercises

8. *Fallacies / Exercises

9. *Invalidity / Exercises

10. *Historical remarks

11. Appendix: list of theorems of chapter III

Chapter IV. 'ALL' and 'SOME' continued

1. Terms and formulas / Exercises

2. Bondage and freedom / Exercises

3. Informal notational conventions / Exercises

4. Translation and symbolization / Exercises

S. Revised inference rules / Exercises

6. Theorems / Exercises

7. Alphabetic variance / Exercises

8. Substitution / Exercises

9. Abbreviated derivations reconsidered / Exercises, Group I, Exercises, Group II, *Exercises, Group III

10. *Invalidity / Exercises

11. *Paradoxical inferences

12. *Historical remarks

13. Appendix: summary of the system of logic developed in chapters I - IV

14. Appendix : list of theorems of chapter IV

*Chapter V. Automatic procedures

1. Introduction

2. Tautologies reconsidered / Exercises

3. Tautological implication; generalised indirect derivation

4. A proof procedure for prenex formulas / Exercises

5. A derivation procedure for prenex arguments / Exercises

6. Conversion to prenex form / Exercises

7. A derivation procedure for arbitrary symbolic arguments / Exercises

8. A decision procedure for certain prenex formulas / Exercises

9. A decision procedure for certain prenex arguments / Exercises

10. Historical remarks

Chapter VI. 'IS' (in one sense)

1. Terms and formulas

2. Translation and symbolization / Exercises

3. Inference rules; theorems / Exercises

4. *Invalidity / Exercises

5. Paradoxical inferences

6. *Historical remarks

7. Appendix: list of theorems of chapter VI

Chapter VII. 'THE'

1. Descriptive phrases, terms, formulas / Exercises

2. Bondage and freedom / Exercises

3. Informal notational conventions / Exercises

4. Translation and symbolization / Exercises

5. Inference rules / Exercises

6. Theorems with unabbreviated proofs / Exercises

7. Alphabetic variance; proper substitution; abbreviated derivations / Exercises

8. Theorems with abbreviated proofs / Exercises

9. Arguments / Exercises

10. *Invalidity / Exercises

11. *Historical remarks

12. Appendix: summary of the system of logic developed in chapters I - VII

13. Appendix: list of theorems of chapter VII

Chapter VIII. Definitions; formal theories

1. The vocabulary of formal languages

2. Bondage and freedom; proper substitution; alphabetic variance

3. Informal notational conventions

4. Derivability

I. Formal theories; the theory of commutative ordered fields

6. Extensions of theories; the theory of real numbers

7. Definitions

Chapter IX. Variable-binding operators

1. Definitions reconsidered

2. The theory of convergence

3. A sketch of further developments

4. *Historical remarks

5. Appendix: list of constants used in chapters VIII and IX

6. Appendix: list of axioms, definitions, and theorems of chapters VIII and IX

BIBLIOGRAPHY

INDEXES