Lucid, non-intimidating presentation of propositional logic, propositional calculus and predicate logic. Accessible to high school students; valuable review of fundamentals for professionals. Exercises (no solutions). Preface. Three appendices. Indices. Bibliogaphy. Includes 14 figures.
| |
| |
| Author's Preface | |
| |
| |
| Introduction | |
| |
| |
| |
| Propositional Logic | |
| |
| |
| |
| Objects and operations | |
| |
| |
| |
| Formulas | |
| |
| |
| Equivalent formulas | |
| |
| |
| Tautologies | |
| |
| |
| |
| Examples of the application of the laws of the logic of propositions in derivations | |
| |
| |
| |
| Normal forms of functions | |
| |
| |
| Minimal forms | |
| |
| |
| |
| Application of the algebra of propositions to the synthesis and analysis of discrete-action networks | |
| |
| |
| |
| The Propositional Calculus | |
| |
| |
| |
| The axiomatic method | |
| |
| |
| The construction of formalized languages | |
| |
| |
| |
| Construction of a propositional calculus (alphabet, formulas, derived formulas) | |
| |
| |
| |
| Consistency, independence, and completeness of a system of axioms in the propositional calculus | |
| |
| |
| |
| Predicate Logic | |
| |
| |
| |
| Sets | |
| |
| |
| Operations on sets | |
| |
| |
| |
| The inadequacy of propositional logic | |
| |
| |
| Predicates | |
| |
| |
| |
| Operations on predicates | |
| |
| |
| Quantifiers | |
| |
| |
| |
| Formulas of predicate logic | |
| |
| |
| Equivalent formulas | |
| |
| |
| Universally valid formulas | |
| |
| |
| |
| Traditional logic (the logic of one-place predicates) | |
| |
| |
| |
| Predicate logic with equality | |
| |
| |
| Axiomatic construction of mathematical theories in the language of predicate logic with equality | |
| |
| |
| |
| A proof of the duality principle for propositional logic | |
| |
| |
| |
| A proof of the deduction theorem for the propositional calculus | |
| |
| |
| |
| A proof of he completeness theorem for the propositional calculus | |
| |
| |
| Bibliography | |
| |
| |
| Index of Special Symbols | |
| |
| |
| Index | |
