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E-raamat: Mathematical Logic for Computer Science 2nd Revised edition [World Scientific e-raamat]

(Chinese Academy Of Science, Beijing, China)
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Mathematical Logic for Computer Science 2nd Revised editionSuurem pilt
Teised raamatud teemal:
World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/3434#t=toc
Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.
Preface v
Introduction 1(4)
1. Prerequisites
5(12)
1.1 Sets
5(6)
1.2 Inductive definitions and proofs
11(4)
1.3 Notations
15(2)
2. Classical Propositional Logic
17(52)
2.1 Propositions and connectives
18(3)
2.2 Propositional language
21(5)
2.3 Structure of formulas
26(7)
2.4 Semantics
33(7)
2.5 Tautological consequence
40(5)
2.6 Formal deduction
45(16)
2.7 Disjunctive and conjunctive normal forms
61(4)
2.8 Adequate sets of connectives
65(4)
3. Classical First-Order Logic
69(40)
3.1 Proposition functions and quantifiers
70(4)
3.2 First-order language
74(9)
3.3 Semantics
83(10)
3.4 Logical consequence
93(4)
3.5 Formal deduction
97(9)
3.6 Prenex normal form
106(3)
4. Axiomatic Deduction System
109(8)
4.1 Axiomatic deduction system
109(3)
4.2 Relation between the two deduction systems
112(5)
5. Soundness and Completeness
117(30)
5.1 Satisfiability and validity
118(7)
5.2 Soundness
125(2)
5.3 Completeness of propositional logic
127(6)
5.4 Completeness of first-order logic
133(4)
5.5 Completeness of first-order logic with equality
137(3)
5.6 Independence
140(7)
6. Compactness, Lowenheim-Skolem and Herbrand Theorems
147(10)
6.1 Compactness Theorem
147(1)
6.2 Lowenheim-Skolem's Theorem
148(1)
6.3 Herbrand's Theorem
149(8)
7. Constructive Logic
157(22)
7.1 Constructivity of proofs
157(2)
7.2 Semantics
159(4)
7.3 Formal deduction
163(8)
7.4 Soundness
171(1)
7.5 Completeness
172(7)
8. Modal Propositional Logic
179(26)
8.1 Modal propositional language
179(1)
8.2 Semantics
180(5)
8.3 Formal deduction
185(7)
8.4 Soundness
192(3)
8.5 Completeness of T
195(3)
8.6 Completeness of S(4), B, S(5)
198(7)
9. Modal First-Order Logic
205(16)
9.1 Modal first-order language
205(1)
9.2 Semantics
206(3)
9.3 Formal deduction
209(2)
9.4 Soundness
211(1)
9.5 Completeness
212(5)
9.6 Equality
217(4)
Appendix (a simple form of formal proof in natural deduction) 221(6)
Bibliography 227(2)
List of Symbols
229(4)
Index 233
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