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E-raamat: First Course in Logic [Taylor & Francis e-raamat]

  • Formaat: 234 pages, 91 Tables, black and white; 81 Illustrations, black and white
  • Ilmumisaeg: 29-Nov-2018
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781351175388
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  • Taylor & Francis e-raamat
  • Hind: 240,04 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
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First Course in LogicSuurem pilt
  • Formaat: 234 pages, 91 Tables, black and white; 81 Illustrations, black and white
  • Ilmumisaeg: 29-Nov-2018
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781351175388
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics — how do we know what we say is true? — and also of computer science — how do I know this program will do what I think it will?

Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability.

Preface ix
Introduction xi
1 Propositional logic
1(102)
1.1 Informal propositional logic
1(8)
1.2 Syntax of propositional logic
9(7)
1.3 Semantics of propositional logic
16(7)
1.4 Logical equivalence
23(8)
1.4.1 Definition
23(2)
1.4.2 Logical patterns
25(2)
1.4.3 Applications
27(4)
1.5 PL in action
31(11)
1.5.1 PL as a programming language
32(4)
1.5.2 PL can be used to model some computers
36(6)
1.6 Adequate sets of connectives
42(3)
1.7 Truth functions
45(3)
1.8 Normal forms
48(8)
1.8.1 Negation normal form (NNF)
48(1)
1.8.2 Disjunctive normal form (DNF)
49(1)
1.8.3 Conjunctive normal form (CNF)
50(1)
1.8.4 Prologue to PROLOG
51(5)
1.9 P = NP? or How to win a million dollars
56(5)
1.10 Valid arguments
61(10)
1.10.1 Definitions and examples
62(4)
1.10.2 Proof in mathematics (I)
66(5)
1.11 Truth trees
71(16)
1.11.1 The truth tree algorithm
72(11)
1.11.2 The theory of truth trees
83(4)
1.12 Sequent calculus
87(16)
1.12.1 Deduction trees
89(5)
1.12.2 Truth trees revisited
94(5)
1.12.3 Gentzen's system LK
99(4)
2 Boolean algebras
103(42)
2.1 More set theory
103(7)
2.2 Boolean algebras
110(10)
2.2.1 Motivation
110(2)
2.2.2 Definition and examples
112(2)
2.2.3 Algebra in a Boolean algebra
114(6)
2.3 Combinational circuits
120(14)
2.3.1 How gates build circuits
120(7)
2.3.2 A simple calculator
127(7)
2.4 Sequential circuits
134(11)
3 First-order logic
145(48)
3.1 First steps
146(27)
3.1.1 Names and predicates
146(2)
3.1.2 Relations
148(2)
3.1.3 Structures
150(2)
3.1.4 Quantification
152(2)
3.1.5 Syntax
154(2)
3.1.6 Variables: their care and maintenance
156(4)
3.1.7 Semantics
160(7)
3.1.8 De Morgan's laws for quantifiers
167(1)
3.1.9 Quantifier examples
168(5)
3.2 Godel's completeness theorem
173(15)
3.2.1 An example
173(1)
3.2.2 Truth trees for FOL
174(6)
3.2.3 The soundness theorem
180(2)
3.2.4 The completeness theorem
182(6)
3.3 Proof in mathematics (II)
188(2)
3.4 Further reading
190(3)
Solutions to all exercises 193(32)
Bibliography 225(6)
Index 231
Mark V. Lawson is a professor in the department of mathematics at Heriot-Watt University. Dr. Lawson has published over 70 papers, and has written four books. His research interests focus on algebraic semigroup theory and its applications.
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