Book:Donald Kalish/Logic: Techniques of Formal Reasoning

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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