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Author's Preface
Introduction

I. Propositional Logic

1. Objects and operations

2. Formulas. Equivalent formulas. Tautologies

3. Examples of the application of the laws of the logic of propositions in derivations

4. Normal forms of functions. Minimal forms

5. Application of the algebra of propositions to the synthesis and analysis of discrete-action networks

II. The Propositional Calculus

1. The axiomatic method. The construction of formalized languages

2. Construction of a propositional calculus (alphabet, formulas, derived formulas)

3. Consistency, independence, and completeness of a system of axioms in the propositional calculus

III. Predicate Logic

1. Sets. Operations on sets

2. The inadequacy of propositional logic. Predicates

3. Operations on predicates. Quantifiers

4. Formulas of predicate logic. Equivalent formulas. Universally valid formulas

5. Traditional logic (the logic of one-place predicates)

6. Predicate logic with equality. Axiomatic construction of mathematical theories in the language of predicate logic with equality

Appendix I. A proof of the duality principle for propositional logic

Appendix II. A proof of the deduction theorem for the propositional calculus

Appendix III. A proof of he completeness theorem for the propositional calculus

Bibliography Index of Special Symbols Index

I. Propositional Logic

1. Objects and operations

2. Formulas. Equivalent formulas. Tautologies

3. Examples of the application of the laws of the logic of propositions in derivations

4. Normal forms of functions. Minimal forms

5. Application of the algebra of propositions to the synthesis and analysis of discrete-action networks

II. The Propositional Calculus

1. The axiomatic method. The construction of formalized languages

2. Construction of a propositional calculus (alphabet, formulas, derived formulas)

3. Consistency, independence, and completeness of a system of axioms in the propositional calculus

III. Predicate Logic

1. Sets. Operations on sets

2. The inadequacy of propositional logic. Predicates

3. Operations on predicates. Quantifiers

4. Formulas of predicate logic. Equivalent formulas. Universally valid formulas

5. Traditional logic (the logic of one-place predicates)

6. Predicate logic with equality. Axiomatic construction of mathematical theories in the language of predicate logic with equality

Appendix I. A proof of the duality principle for propositional logic

Appendix II. A proof of the deduction theorem for the propositional calculus

Appendix III. A proof of he completeness theorem for the propositional calculus

Bibliography Index of Special Symbols Index

Library of Congress subject headings for this publication: Logic, Symbolic and mathematical