# Book:Donald Kalish/Logic: Techniques of Formal Reasoning

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## Donald Kalish and Richard Montague:

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

Published $1964$, **Harcourt Brace Jovanovich, Inc.**

- ISBN 0-15-551180-7.

### Subject Matter

### 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