Book:Donald Kalish/Logic: Techniques of Formal Reasoning

Subject Matter

 * Logic

Contents

 * Preface
 * Chapter $\text {I}$. 'NOT' and 'IF'
 * 1. Symbols and sentences /
 * 2. From symbols to English and back /
 * 3. Derivability and validity /
 * 4. *Fallacies
 * 5. Theorems /
 * 6. *Historical remarks


 * Chapter $\text {II}$. 'AND', 'OR', 'IF AND ONLY IF'
 * 1. Symbols and sentences /
 * 2. Translation and symbolization /
 * 3. Inference rules; theorems with unabbreviated proofs /
 * 4. Abbreviated derivations /
 * 5. Theorems with abbreviated proofs /
 * 6. *Truth-value analysis of sentences /
 * 7. *Truth-value analysis of arguments /
 * 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 /
 * 2. Bondage and freedom /
 * 3. Informal notational conventions
 * 4. Translation and symbolization /
 * 5. Inference rules and forms of derivation; theorems with unabbreviated proofs /
 * 6. Abbreviated derivations; theorems with abbreviated proofs /
 * 7. Arguments /
 * 8. *Fallacies /
 * 9. *Invalidity /
 * 10. *Historical remarks
 * 11. Appendix: list of theorems of chapter $\text {III}$


 * Chapter $\text {IV}$. 'ALL' and 'SOME' continued
 * 1. Terms and formulas /
 * 2. Bondage and freedom /
 * 3. Informal notational conventions /
 * 4. Translation and symbolization /
 * S. Revised inference rules /
 * 6. Theorems /
 * 7. Alphabetic variance /
 * 8. Substitution /
 * 9. Abbreviated derivations reconsidered /
 * 10. *Invalidity /
 * 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 /
 * 3. Tautological implication; generalised indirect derivation
 * 4. A proof procedure for prenex formulas /
 * 5. A derivation procedure for prenex arguments /
 * 6. Conversion to prenex form /
 * 7. A derivation procedure for arbitrary symbolic arguments /
 * 8. A decision procedure for certain prenex formulas /
 * 9. A decision procedure for certain prenex arguments /
 * 10. Historical remarks


 * Chapter $\text {VI}$. 'IS' (in one sense)
 * 1. Terms and formulas
 * 2. Translation and symbolization /
 * 3. Inference rules; theorems /
 * 4. *Invalidity /
 * 5. Paradoxical inferences
 * 6. *Historical remarks
 * 7. Appendix: list of theorems of chapter $\text {VI}$


 * Chapter $\text {VII}$. 'THE'
 * 1. Descriptive phrases, terms, formulas /
 * 2. Bondage and freedom /
 * 3. Informal notational conventions /
 * 4. Translation and symbolization /
 * 5. Inference rules /
 * 6. Theorems with unabbreviated proofs /
 * 7. Alphabetic variance; proper substitution; abbreviated derivations /
 * 8. Theorems with abbreviated proofs /
 * 9. Arguments /
 * 10. *Invalidity /
 * 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 $\text {IX}$







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