عنوان

Handbook of Logic and Proof Techniques for Computer Science

1461201152

9781461201151

b542272

Handbook of Logic and Proof Techniques for Computer Science

[Book]

by Steven G. Krantz.

Boston, MA

Birkhäuser Boston : Imprint : Birkhäuser

2002

(xix, 245 pages)

1 Notation and First-Order Logic --;1.1 The Use of Connectives --;1.2 Truth Values and Truth Tables --;1.3 The Use of Quantifiers --;1.4 Gödel's Completeness Theorem --;1.5 Second-Order Logic --;2 Semantics and Syntax --;2.1 Elementary Symbols --;2.2 Well-Formed Formulas or wffs [Syntax] --;2.3 Free and Bound Variables (Syntax) --;2.4 The Semantics of First-Order Logic --;3 Axiomatics and Formalism in Mathematics --;3.1 Basic Elements --;3.2 Models --;3.3 Consistency --;3.4 Gödel's Incompleteness Theorem --;3.5 Decidability and Undecidability --;3.6 Independence --;4 The Axioms of Set Theory --;4.1 Introduction --;4.2 Axioms and Discussion --;4.3 Concluding Remarks --;5 Elementary Set Theory --;5.1 Set Notation --;5.2 Sets, Subsets, and Elements --;5.3 Binary Operations on Sets --;5.4 Relations and Equivalence Relation --;5.5 Equivalence Relations --;5.6 Number Systems --;5.7 Functions --;5.8 Cardinal Numbers --;5.9 A Word About Classes --;5.10 Fuzzy Set Theory --;5.11 The Lambda Calculus --;5.12 Sequences --;5.13 Bags --;6 Recursive Functions --;6.1 Introductory Remarks --;6.2 Primitive Recursive Functions --;6.3 General Recursive Functions --;7 The Number Systems --;7.1 The Natural Numbers --;7.2 The Integers --;7.3 The Rational Numbers --;7.4 The Real Numbers --;7.5 The Complex Numbers --;7.6 The Quaternions --;7.7 The Cayley Numbers --;7.8 Nonstandard Analysis --;8 Methods of Mathematical Proof --;8.1 Axiomatics --;8.2 Proof by Induction --;8.3 Proof by Contradiction --;8.4 Direct Proof --;8.5 Other Methods of Proof --;9 The Axiom of Choice --;9.1 Enunciation of the Axiom --;9.2 Examples of the Use of the Axiom of Choice --;9.3 Consequences of the Axiom of Choice --;9.4 Paradoxes --;9.5 The Countable Axiom of Choice --;9.6 Consistency of the Axiom of Choice --;9.7 Independence of the Axiom of Choice --;10 Proof Theory --;10.1 General Remarks --;10.2 Cut Elimination --;10.3 Propositional Resolution --;10.4 Interpolation --;10.5 Finite Type --;10.6 Beth's Definability Theorem --;11 Category Theory --;11.1 Introductory Remarks --;11.2 Metacategories and Categories --;12 Complexity Theory --;12.1 Preliminary Remarks --;12.2 Polynomial Complexity --;12.3 Exponential Complexity --;12.4 Two Tables for Complexity Theory --;12.5 Problems of Class P --;12.6 Problems of Class NP --;12.7 NP-Completeness --;12.8 Cook's Theorem --;12.9 Examples of NP-Complete Problems --;12.10 More on P/NP --;12.11 Descriptive Complexity Theory --;13 Boolean Algebra --;13.1 Description of Boolean Algebra --;13.2 Axioms of Boolean Algebra --;13.3 Theorems in Boolean Algebra --;13.4 Illustration of the Use of Boolean Logic --;14 The Word Problem --;14.1 Introductory Remarks --;14.2 What Is a Group? --;14.3 What Is a Free Group? --;14.4 The Word Problem --;14.5 Relations and Generators --;14.6 Amalgams --;14.7 Description of the Word Problem --;List of Notation from Logic --;Glossary of Terms from Mathematical and Sentential Logic --;A Guide to the Literature.

Logic is, and should be, the core subject area of modern mathemat- ics. There is need for a book that introduces important logic terminology and concepts to the working mathematical scientist who has only a passing acquaintance with logic.

Computer science.

Logic design.

Mathematics.

by Steven G. Krantz.

Steven G Krantz

[Book]

Y