عنوان

Handbook of Logic and Proof Techniques for Computer Science

شابک

1461201152

شابک

9781461201151

شماره

b542272

عنوان اصلي

Handbook of Logic and Proof Techniques for Computer Science

نام عام مواد

[Book]

نام نخستين پديدآور

by Steven G. Krantz.

محل نشرو پخش و غیره

Boston, MA

نام ناشر، پخش کننده و غيره

Birkhäuser Boston : Imprint : Birkhäuser

تاریخ نشرو بخش و غیره

2002

نام خاص و کميت اثر

(xix, 245 pages)

متن يادداشت

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.

متن يادداشت

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.

موضوع مستند نشده

Computer science.

موضوع مستند نشده

Logic design.

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Steven G. Krantz.

مستند نام اشخاص تاييد نشده

Steven G Krantz

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y