Elementary Logic : For Software Development

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Elementary Logic : For Software Development

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 305 p.
  • 言語 ENG
  • 商品コード 9781848000810
  • DDC分類 005.101

Table of Contents

  Part I Language and Logical From
Atomic Statements 3 (10)
Vagueness and Ambiguity 3 (1)
Logical English 4 (1)
Names 5 (1)
Predicates 6 (1)
Descriptions 7 (1)
Atomic Statements 8 (5)
Compound Statements 13 (10)
Truth Functional Connectives 13 (4)
Statements with Multiple Connectives 17 (1)
Parenthesis Dropping Conventions 18 (5)
Quantified Statements 23 (10)
Logical Variables 23 (2)
Conditions 25 (2)
Open Descriptions 27 (1)
Quantifiers 28 (5)
Expressing Arguments 33 (8)
Arguments 33 (1)
Deductive and Inductive Arguments 34 (1)
Some Practical Suggestions 35 (3)
Expressing the Logical Structures of 38 (3)
Arguments
Defining Data Structures 41 (12)
Properties of the Identity Relation 42 (1)
Identity is Reflexive, Symmetric, and 42 (1)
Transitive
Leibniz's Law 42 (1)
Defining Data Structures 43 (10)
Sets 43 (2)
Bags 45 (1)
Sequences 46 (1)
Relations 47 (1)
Functions 48 (2)
Stacks 50 (1)
1-Dimensional Arrays 51 (2)
Expressing Problem Specifications 53 (14)
Functional Problem Specifications 53 (2)
What Can Go Wrong with Problem 55 (4)
Specifications
Expressing Problem Specifications with 59 (8)
Logical English
Expressing Program Designs 67 (12)
Pseudocode for Instructions 67 (4)
Atomic Instructions 68 (1)
Compound Instructions 68 (3)
Pseudocode for Algorithms 71 (8)
Part II Material Truth
Truth for Statements with at Most One 79 (16)
Connective
The Laws of Excluded Middle and 80 (1)
Noncontradiction
Atomic Statements 80 (1)
Truth Functional Connectives 81 (5)
Negation 82 (1)
Conjunction 82 (1)
Disjunction: Inclusive and Exclusive 83 (1)
Material Equivalence 83 (2)
Material Implication 85 (1)
Conditions 86 (1)
Quantified Statements 87 (1)
Summary of Material Truth Conditions 88 (1)
Some Applications 89 (6)
Short Cut Evaluation: ``cand'' and 89 (1)
``cor''
Bitwise Extensions of Truth Functions 90 (5)
Truth for Statements with Multiple 95 (10)
Connectives
Compound Statements 95 (5)
Computing Truth Values of Compound 96 (2)
Statements
Reducing the Need for Parentheses 98 (2)
How to Make Truth Tables for Compound 100(3)
Statements
The Four Parts of a Truth Table 100(1)
Organizing a Truth Table Calculation 101(2)
Reading Truth Tables from Right to Left 103(2)
Tracing Program Execution 105(10)
Tracing Program Execution Forwards 105(4)
Event Trace Tables 106(1)
Value Trace Tables 107(1)
Tracing with Complex Conditions 108(1)
Tracing Program Execution Backwards 109(6)
Part III Logical Truth
Truth Functional Forms 115(14)
Overview 115(2)
Truth Functional Forms 117(1)
Interpretations of Truth Functional Forms 118(1)
Truth Under an Interpretation 119(1)
Truth Functional Truth, Falsity, and 119(2)
Contingency
Using Forms to Find the Logical Status of 121(3)
English Statements
Application to Simplifying Statements and 124(5)
Conditions
Truth Functional Properties of Program 129(10)
Designs
The General From of Decision Tables 129(1)
Limited Entry Decision Tables 130(3)
The Basic Form 130(1)
Simplifying Tables with ``Don't Care'' 131(2)
Condition Entries
Extended Entry Decision Tables 133(2)
Decision Tables and Other Control 135(1)
Structures
Consistency, Completeness, and Redundancy 136(3)
of Decision Tables
Quantified Forms 139(14)
How Truth Functional Logic Differs from 139(1)
Quantificational Logic
Well Formed Forms 140(2)
Interpretations of Wffs 142(1)
Truth of Wffs in an Interpretation 143(2)
Logical Truth of Wffs 145(3)
Using Wffs to Determine the Logical 148(1)
Status of English Statements
Conditions Revisited 149(2)
Summary of Classifications 151(2)
Logical Equivalence 153(12)
Truth Functional Equivalence 154(1)
Applications of Truth Functional 155(4)
Equivalence
Equivalence and Simplification of 155(3)
Program Instructions
Equivalence and Simplification of SQL 158(1)
Select Instructions
Logical Equivalence 159(4)
Logical Equivalence of Wffs 159(1)
Logical Equivalence of Conditions 160(3)
Applications of Logical Equivalence 163(2)
Simplification of Problem Specifications 163(1)
Detecting Redundancy 163(2)
Logical Implication and Validity 165(16)
Logical Implication and Validity 166(3)
Logical Implication 166(1)
Logical Validity 166(1)
Soundness 166(3)
Determining Validity 169(12)
Degrees of Formality 169(1)
Arguments and Corresponding Conditionals 170(1)
Truth Functional Validity 171(6)
Logical Validity 177(4)
Rules of Inference 181(8)
Limitations of Truth Table Tests 181(1)
Rules of Inference 182(1)
Formal Rules of Inference 182(1)
Correct and Incorrect Rules of Inference 182(1)
Some Truth Functional Rules of Inference 183(6)
Examples of Correct Rules of Inference 183(2)
Some Properties of Rules of Inference 185(3)
Examples of Incorrect Rules of 188(1)
Inference (Formal Fallacies)
Proof 189(14)
Kinds of Proof 190(1)
Different Senses of Proof 190(1)
Formal vs Informal Proofs 190(1)
Two Ways of Organizing Proofs 191(2)
Three Proof Strategies 193(5)
Direct Proof 193(2)
Conditional Proof 195(1)
Indirect Proof 196(2)
Applying Logic to Specific Subjects 198(5)
Using Instances of General Forms 198(1)
Adding Nonlogical Justifications 199(4)
Algorithmic Unsolvability Proofs 203(8)
Algorithmic Solvability and Unsolvability 203(4)
The Halting Problem is Algorithmically 207(1)
Unsolvable
Other Algorithmically Unsolvable Problems 208(3)
Program Correctness Proofs 211(22)
The Limits of Testing 211(1)
Proofs Expressed in English Prose 212(4)
Proofs Using Floyd's Method of Invariant 216(3)
Assertions
Rules of Inference Involving Algorithms 219(5)
Notation for Statements Involving 220(1)
Instructions
The Assignment Rule 220(2)
Rules of Inference about Control 222(2)
Structures
Proofs Using Rules of Inference 224(9)
Above and Beyond this Book 233(8)
Other Texts on Classical Logic 234(1)
Standard Texts 234(1)
Computer Oriented Texts 234(1)
Extensions of Classical Logic 234(1)
Floyd-Hoare Logic 234(1)
Temporal, Modal, and Dynamic Logics 235(1)
Rivals to Classical Logic 235(1)
Applications of Logic to Computing or 235(2)
Computing to Logic
Logic Circuits 235(1)
3-Valued Logic and SQL 235(1)
More on Expressing and Using 235(1)
Specifications
Logic Testing of Software 236(1)
Computability and Algorithmic 236(1)
Unsolvability
AI and Computer Aided Reasoning 236(1)
Quantum Computing and Programming 237(1)
Programming Challenges 237(4)
Solutions to Selected Exercises 241(64)
Chapter 1 241(2)
Chapter 2 243(3)
Chapter 3 246(3)
Chapter 4 249(2)
Chapter 5 251(3)
Chapter 6 254(3)
Chapter 7 257(2)
Chapter 8 259(2)
Chapter 9 261(4)
Chapter 10 265(5)
Chapter 11 270(4)
Chapter 12 274(3)
Chapter 13 277(3)
Chapter 14 280(6)
Chapter 15 286(5)
Chapter 16 291(2)
Chapter 17 293(6)
Chapter 18 299(1)
Chapter 19 300(5)
Sources and Bibliography 305(4)
Index 309