First Course in Mathematical Logic - Brossura

Suppes, Patrick; Hill, Shirley A.

Brossura

ISBN 10: 0486422593 ISBN 13: 9780486422596

Casa editrice: Dover Pubns, 2003

Riassunto

In modern mathematics, both the theory of proof and the derivation of theorems from axioms bear an unquestioned importance. The necessary skills behind these methods, however, are frequently underdeveloped. This book counters that neglect with a rigorous introduction that is simple enough in presentation and context to permit relatively easy comprehension. It comprises the sentential theory of inference, inference with universal quantifiers, and applications of the theory of inference developed to the elementary theory of commutative groups. Throughout the book, the authors emphasize the pervasive and important problem of translating English sentences into logical or mathematical symbolism. Their clear and coherent style of writing ensures that this work may be used by students in a wide range of ages and abilities.

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Contenuti

1. Symbolizing Sentences 1.1 Sentences 1.2 Sentential Connectives 1.3 The Form of Molecular Sentences 1.4 Symbolizing Sentences 1.5 The Sentential Connectives and Their Symbols--Or; Not; If . . . then . . . 1.6 Grouping and Parentheses. The Negation of a Molecular Sentence 1.7 Elimination of Some Parentheses 1.8 Summary 2. Logical Inference 2.1 Introduction 2.2 Rules of Inference and Proof Modus Ponendo Ponens Proofs Two-Step Proofs Double Negation Modus Tollendo Tollens More on Negation Adjunction and Simplification Disjunctions as Premises Modus Tollendo Ponens 2.3 Sentential Derivation 2.4 More About Parentheses 2.5 Further Rules of Inference Law of Addition Law of Hypothetica Syllogism Law of Disjunctive Syllogism Law of Disjunctive Simplification Commutative Laws De Morgan's Laws 2.6 Biconditional Sentences 2.7 Summary of Rules of Inference. Table of Rules of Inference 3. Truth and Validity 3.1 Introduction 3.2 Truth Value and Truth-Functional Connectives Conjunction Negation Disjunction Conditional Sentences Equivalence: Biconditional Sentences 3.3 Diagrams of Truth Value 3.4 Invalid Conclusions 3.5 Conditional Proof 3.6 Consistency 3.7 Indirect Proof 3.8Summary 4. Truth Tables 4.1 Truth Tables 4.2 Tautologies 4.3 Tautological Implication and Tautological Equivalence 4.4 Summary 5. Terms, Predicates, and Universal Quantifiers 5.1 Introduction 5.2 Terms 5.3 Predicates 5.4 Common Nouns as Predicates 5.5 Atomic Formulas and Variables 5.6 Universal Quantifiers 5.7 Two Standard Forms 6. Universal Specification and Laws of Identity 6.1 One Quantifier 6.2 Two or More Quantifiers 6.3 Logic of Identity 6.4 Truths of Logic 7. A Simple Mathematical System: Axioms for Addition 7.1 Commutative Axiom 7.2 Associative Axiom 7.3 Axiom for Zero 7.4 Axiom for Negative Numbers 8. Universal Generalization 8.1 Theorems with Variables 8.2 Theorems with Universal Quantifiers Index

Product Description

Starting with symbolizing sentences and sentential connectives, this work proceeds to the rules of logical inference and sentential derivation, examines the concepts of truth and validity, and presents a series of truth tables. Subsequent topics include terms, predicates, and universal quantifiers; universal specification and laws of identity; axioms for addition; and universal generalization. 1964 edition. Index.

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 0486422593
• ISBN 13: 9780486422596
• Rilegatura: Copertina flessibile
• Numero di pagine: 274
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia