Book:Donald Kalish/Logic: Techniques of Formal Reasoning

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



Source work progress
* : $\text{III}$: 'ALL' and 'SOME': $\S 1$