This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals.
Author(s): Abram Aronovich Stolyar
Series: Dover books on Advance Mathematics
Publisher: Dover Publications
Year: 1983
Language: English
Pages: 209
City: New York
Author's Preface
Contents
INTRODUCTION
1 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
2 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
3 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
APPENDIXES
I A PROOF OF THE DUALITY PRINCIPLE FOR PROPOSITIONAL LOGIC
II A PROOF OF THE DEDUCTION THEOREM FOR THE PROPOSITIONAL CALCULUS
III A PROOF OF THE COMPLETENESS THEOREM FOR THE PROPOSITIONAL CALCULUS
BIBLIOGRAPHY
INDEX OF SPECIAL SYMBOLS
INDEX
