Book:Donald Kalish/Logic: Techniques of Formal Reasoning

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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


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