Elementary Logic : For Software Development

For Software Development

By: Robert Lover

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Paperback | 1 August 2008

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328 Pages

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23.5 x 15.24 x 1.91

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The ability to reason correctly is critical to most aspects of computer science and to software development in particular. Since logic is the discipline concerned with the general rules and criteria of correct reasoning anyone involved with computer science and software development will benefit from studying logic and its applications to computing.

Features: Covers elementary logic and its application to most stages of software development, discusses the application of logic to the English language, as software development begins usually with problems described by end users in ordinary English, emphasizes truth functional logic as well as quantificational logic, includes various examples and exercises to enable independent self-study.

This book provides a reader friendly foundation and offers valuable insight into the topic, serving as a helpful reference for practitioners and advanced students involved with software development.

Industry Reviews

From the reviews: "Logic deserves to be more widely taught on its merits, not just as a byproduct of special needs. This book does exactly that. The author aims the book at software developers and computer science students, but it could very well be used in other settings, as well. ! used by teachers and instructors in a variety of settings, according to personal interest or departmental needs. ! The book is well organized and well written. ! I liked the book and I recommend it." (Edgar R. Chavez, ACM Computing Reviews, April, 2009)

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Non-Fiction Philosophy Computing & I.T.Computer Programming & Software Development Software Engineering Mathematics Mathematical Foundation Mathematical Logic Computer Science Computer Architecture & Logic Design

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

Elementary Logic : For Software Development

For Software Development

At a Glance

Paperback

Industry Reviews

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You Can Find This Book In

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