An Introduction to Logical Theory

ISBN-13: 9781551119939 / Angielski / Miękka / 2013 / 440 str.

Aladdin M. Yaqub

Opis

An introduction to the concepts and methods of logic that grounds the classical systems in their underlying theory.

Spis treści

Introduction and Instructor’s Guide

Chapter One: Informal Logic
1.1 Taxonomy of Arguments

1. Definition of an argument
2. Types of link
3. Deductively valid and invalid arguments
4. Deductively sound and unsound arguments
5. Deductive logic
6. Deductive Arguments
7. Probabilistic arguments
8. Probabilistic logic
9. Cogent arguments

1.2 Classical Deductive Logic and the Notion of Logical Possibility

1. Definition of a logical possibility
2. Classical truth values and bivalence
3. Deductive validity and logical consequence
4. Definition of deductive validity
5. Definition of deductive invalidity
6. Definition of logical truth
7. Definition of logical falsehood
8. Definition of contingency
9. Definition of logical equivalence
10. Definition of consistency
11. Definition of inconsistency
12. Relevant logical possibilities
13. Examples and counterexamples

1.3 Exercises
Solutions to the Starred Exercises

Chapter Two: Term Logic (TL)

2.1 The TL Worldview
2.2 The Syntax of TL

1. The basic vocabulary of TL
2. TL sentences
3. Non-recursive generative grammar

2.3 Translating English into TL

1. General terms
2. Singular terms
3. Universal and existential quantifiers
4. Translating English idioms into TL

2.4 The Semantics of TL

1. TL diagrams
2. Similar TL diagrams
3. The truth conditions of TL sentences
4. Truth values of TL sentences on similar TL diagrams

2.5 Logical Concepts in TL

1. Definition of a TL argument
2. Logical possibilities and TL diagrams
3. Definition of deductive validity in TL
4. Definition of deductive invalidity in TL
5. Definition of logical truth in TL
6. Definition of logical falsehood in TL
7. Definition of contingency in TL
8. Definition of logical equivalence in TL
9. Definition of consistency in TL
10. Definition of inconsistency in TL
11. The decidability of logical concepts in TL
12. The representability of logical possibilities by TL diagrams

2.6 Exercises
Solutions to the Starred Exercises

Chapter Three: Sentence Logic (SL)

3.1 The SL Worldview
3.2 The Syntax of SL

1. The basic vocabulary of SL
2. SL sentences
3. Types of SL compound sentences
4. SL construction trees
5. A convention
6. Generative recursive grammar

3.3 Translating English into SL

1. Translating English connectives into SL connectives
2. Translating English idioms into SL

3.4 The Semantics of SL

1. SL truth valuations
2. The truth conditions of SL sentences
3. Truth tables
4. Truth analysis

3.5 Logical Concepts in SL

1. Definition of an SL argument
2. Logical possibilities and SL truth valuations
3. Definition of deductive validity in SL
4. Definition of deductive invalidity in SL
5. Definition of logical truth in SL
6. Definition of logical falsehood in SL
7. Definition of contingency in SL
8. Definition of logical equivalence in SL
9. Definition of consistency in SL
10. Definition of inconsistency in SL
11. The decidability of logical concepts in SL
12. The representability of logical possibilities by SL truth valuations

3.6 Exercises
Solutions to the Starred Exercises

Chapter Four: Predicate Logic (PL)

4.1 The PL Worldview
4.2 The Syntax of PL

1. The basic vocabulary of PL
2. PL quantifiers and PL terms
3. PL formulas
4. Bound and free variables and PL sentences
5. PL construction trees
6. Three conventions
7. Generative recursive grammar

4.3 Translating PL into English and English into PL
4.4 The Semantics of PL

1. PL interpretations
2. The size of a PL interpretation
3. The truth conditions of PL sentences
4. Bivalence and classical truth

4.5 Logical Concepts in PL

1. Definition of a PL argument
2. Logical possibilities and PL interpretations
3. Definition of deductive validity in PL
4. Definition in deductive invalidity in PL
5. Definition of logical truth in PL
6. Definition of logical falsehood in PL
7. Definition of contingency in PL
8. Definition of logical equivalence in PL
9. Definition of consistency in PL
10. Definition of inconsistency in PL
11. The undecidability of logical concepts in PL
12. The relation between TL and PL and the relation between SL and PL
13. The representability of logical possibilities by PL interpretations

4.6 Exercises
Solutions to the Starred Exercises

Chapter Five: Classical Proof Theory

5.1 The Notion of Demonstrative Proof
5.2 The Notion of Formal Derivation

1. Definition of a formal derivation
2. The Soundness Theorem for PL
3. The Completeness Theorem for PL
4. Corollaries of the Soundness and Completeness Theorems
5. The Compactness Theorem

5.3 The Natural Deduction System (NDS)

1. Types of NDS rules
2. The NDS rules of inference
3. The Gentzen Deduction System (GDS)

5.4 Strategies for Constructing Formal Derivations
5.5 Exercises
Solutions to the Starred Exercises

Index