Elementary Logic

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Elementary Logic / Robert Lover

資料種別:: 電子ブック
出版情報:: SpringerLink Books - AutoHoldings
Springer London, 2008
著者名:: Lover, Robert
ISBN:: 9781848000810 [1848000812]
9781848000827 [1848000820]
書誌ID:: OB00492863

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言語:

英語

目次情報:

Language and Logical Form / Part I：

Atomic Statements / 1：

Vagueness and Ambiguity / 1.1：

Logical English / 1.2：

Names / 1.3：

Predicates / 1.4：

Descriptions / 1.5：

Compound Statements / 1.6：

Truth Functional Connectives / 2.1：

Statements with Multiple Connectives / 2.2：

Parenthesis Dropping Conventions / 2.3：

Quantified Statements / 3：

Logical Variables / 3.1：

Conditions / 3.2：

Open Descriptions / 3.3：

Quantifiers / 3.4：

Expressing Arguments / 4：

Arguments / 4.1：

Deductive and Inductive Arguments / 4.2：

Some Practical Suggestions / 4.3：

Expressing the Logical Structures of Arguments / 4.4：

Defining Data Structures / 5：

Properties of the Identity Relation / 5.1：

Identity is Reflexive, Symmetric, and Transitive / 5.1.1：

Leibniz's Law / 5.1.2：

Sets / 5.2：

Bags / 5.2.2：

Sequences / 5.2.3：

Relations / 5.2.4：

Functions / 5.2.5：

Stacks / 5.2.6：

1-Dimensional Arrays / 5.2.7：

Expressing Problem Specifications / 6：

Functional Problem Specifications / 6.1：

What Can Go Wrong with Problem Specifications / 6.2：

Expressing Problem Specifications with Logical English / 6.3：

Expressing Program Designs / 7：

Pseudocode for Instructions / 7.1：

Atomic Instructions / 7.1.1：

Compound Instructions / 7.1.2：

Pseudocode for Algorithms / 7.2：

Material Truth / Part II：

Truth for Statements with at Most One Connective / 8：

The Laws of Excluded Middle and Noncontradiction / 8.1：

Negation / 8.2：

Conjunction / 8.3.2：

Disjunction: Inclusive and Exclusive / 8.3.3：

Material Equivalence / 8.3.4：

Material Implication / 8.3.5：

Summary of Material Truth Conditions / 8.4：

Some Applications / 8.7：

Short Cut Evaluation: "cand" and "cor" / 8.7.1：

Bitwise Extensions of Truth Functions / 8.7.2：

Truth for Statements with Multiple Connectives / 9：

Computing Truth Values of Compound Statements / 9.1：

Reducing the Need for Parentheses / 9.1.2：

How to Make Truth Tables for Compound Statements / 9.2：

The Four Parts of a Truth Table / 9.2.1：

Organizing a Truth Table Calculation / 9.2.2：

Reading Truth Tables from Right to Left / 9.3：

Tracing Program Execution / 10：

Tracing Program Execution Forwards / 10.1：

Event Trace Tables / 10.1.1：

Value Trace Tables / 10.1.2：

Tracing with Complex Conditions / 10.1.3：

Tracing Program Execution Backwards / 10.2：

Logical Truth / Part III：

Truth Functional Forms / 11：

Overview / 11.1：

Interpretations of Truth Functional Forms / 11.2：

Truth Under an Interpretation / 11.4：

Truth Functional Truth, Falsity, and Contingency / 11.5：

Using Forms to Find the Logical Status of English Statements / 11.6：

Application to Simplifying Statements and Conditions / 11.7：

Truth Functional Properties of Program Designs / 12：

The General Form of Decision Tables / 12.1：

Limited Entry Decision Tables / 12.2：

The Basic Form / 12.2.1：

Simplifying Tables with "Don't Care" Condition Entries / 12.2.2：

Extended Entry Decision Tables / 12.3：

Decision Tables and Other Control Structures / 12.4：

Consistency, Completeness, and Redundancy of Decision Tables / 12.5：

Quantified Forms / 13：

How Truth Functional Logic Differs from Quantificational Logic / 13.1：

Well Formed Forms / 13.2：

Interpretations of Wffs / 13.3：

Truth of Wffs in an Interpretation / 13.4：

Logical Truth of Wffs / 13.5：

Using Wffs to Determine the Logical Status of English Statements / 13.6：

Conditions Revisited / 13.7：

Summary of Classifications / 13.8：

Logical Equivalence / 14：

Truth Functional Equivalence / 14.1：

Applications of Truth Functional Equivalence / 14.2：

Equivalence and Simplification of Program Instructions / 14.2.1：

Equivalence and Simplification of SQL Select Instructions / 14.2.2：

Logical Equivalence of Wffs / 14.3：

Logical Equivalence of Conditions / 14.3.2：

Applications of Logical Equivalence / 14.4：

Simplification of Problem Specifications / 14.4.1：

Detecting Redundancy / 14.4.2：

Logical Implication and Validity / 15：

Logical Implication / 15.1：

Logical Validity / 15.1.2：

Soundness / 15.1.3：

Determining Validity / 15.2：

Degrees of Formality / 15.2.1：

Arguments and Corresponding Conditionals / 15.2.2：

Truth Functional Validity / 15.2.3：

Rules of Inference / 15.2.4：

Limitations of Truth Table Tests / 16.1：

Formal Rules of Inference / 16.2：

Correct and Incorrect Rules of Inference / 16.2.2：

Some Truth Functional Rules of Inference / 16.3：

Examples of Correct Rules of Inference / 16.3.1：

Some Properties of Rules of Inference / 16.3.2：

Examples of Incorrect Rules of Inference (Formal Fallacies) / 16.3.3：

Proof / 17：

Kinds of Proof / 17.1：

Different Senses of Proof / 17.1.1：

Formal vs Informal Proofs / 17.1.2：

Two Ways of Organizing Proofs / 17.2：

Three Proof Strategies / 17.3：

Direct Proof / 17.3.1：

Conditional Proof / 17.3.2：

Indirect Proof / 17.3.3：

Applying Logic to Specific Subjects / 17.4：

Using Instances Of General Forms / 17.4.1：

Adding Nonlogical Justifications / 17.4.2：

Algorithmic Unsolvability Proofs / 18：

Algorithmic Solvability and Unsolvability / 18.1：

The Halting Problem is Algorithmically Unsolvable / 18.2：

Other Algorithmically Unsolvable Problems / 18.3：

Program Correctness Proofs / 19：

The Limits of Testing / 19.1：

Proofs Expressed in English Prose / 19.2：

Proofs Using Floyd's Method of Invariant Assertions / 19.3：

Rules of Inference Involving Algorithms / 19.4：

Notation for Statements Involving Instructions / 19.4.1：

The Assignment Rule / 19.4.2：

Rules of Inference about Control Structures / 19.4.3：

Proofs Using Rules of Inference / 19.5：

Above and Beyond this Book / 20：

Other Texts on Classical Logic / 20.1：

Standard Texts / 20.1.1：

Computer Oriented Texts / 20.1.2：

Extensions of Classical Logic / 20.2：

Floyd-Hoare Logic / 20.2.1：

Temporal, Modal, and Dynamic Logics / 20.2.2：

Rivals to Classical Logic / 20.3：

Applications of Logic to Computing or Computing to Logic / 20.4：

Logic Circuits / 20.4.1：

3-Valued Logic and SQL / 20.4.2：

More on Expressing and Using Specifications / 20.4.3：

Logic Testing of Software / 20.4.4：

Computability and Algorithmic Unsolvability / 20.4.5：

AI and Computer Aided Reasoning / 20.4.6：

Quantum Computing and Programming / 20.4.7：

Programming Challenges / 20.5：

Solutions to Selected Exercises

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Sources and Bibliography

Index

Language and Logical Form / Part I：

Atomic Statements / 1：

Vagueness and Ambiguity / 1.1：

Logical English / 1.2：

Names / 1.3：

Predicates / 1.4：

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