INTRODUCTION TO ELEMENTARY MATHEMATICAL LOGIC

Stolyar, Abram Aronovich

ISBN 10: 0486645614 ISBN 13: 9780486645612

Editore: New York, Dover 1983, 2010

Lingua: Inglese

Condizione: Usato Brossura

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Dati bibliografici

Titolo

INTRODUCTION TO ELEMENTARY MATHEMATICAL LOGIC

Editore

New York, Dover 1983

Data di pubblicazione

2010

Lingua

Inglese

ISBN 10

0486645614

ISBN 13

9780486645612

Rilegatura

Soft cover

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Descrizione articolo

Riassunto

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. 1970 edition.

Contenuti

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

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