# 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 $\text {1964}$, **Harcourt Brace Jovanovich, Inc.**

- ISBN 0-15-551180-7

### Subject Matter

### Contents

- Preface
- Chapter $\text {I}$. '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 $\text {II}$. '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 $\text {I}$ and $\text {II}$

- Chapter $\text {III}$. '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 $\text {III}$

- Chapter $\text {IV}$. '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 $\text {I}$ - $\text {IV}$
- 14. Appendix : list of theorems of chapter $\text {IV}$

- *Chapter $\text {V}$. 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 $\text {VI}$. '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 $\text {VI}$

- Chapter $\text {VII}$. '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 $\text {I}$ - $\text {VII}$
- 13. Appendix: list of theorems of chapter $\text {VII}$

- Chapter $\text {VIII}$. 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 $\text {IX}$. 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 $\text {VIII}$ and $\text {IX}$
- 6. Appendix: list of axioms, definitions, and theorems of chapters $\text {VIII}$ and $\text {IX}$

- Bibliography

- Indexes

## Source work progress

- 1964: Donald Kalish and Richard Montague:
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