Contents
Introduction - logic and logical form
What does logic do?
Logical inference and logical form
Logical words
A brief history of logic
Modern logic
1.
Propositional logic
1.1
Conjunction, negation, disjunction
What does propositional logic do?
Propositions and truth values
Atomic and compound sentences
Conjunction
Negation
Disjunction
Exercises
1.2
Conditional and biconditional
Conditional
Biconditional
A systematic way to symbolize natural language sentences
Exercises
1.3
Truth tables
Syntax of propositional logic
Semantics of propositional logic. Truth tables
Exercises
1.4
Indirect proof
Exercises
1.5
Truth-value analysis
Exercises
1.6
Logical inference and logical equivalence
Logical inference
Logical equivalence
Exercises
1.7
Quick test of logical inference
Exercises
1.8
Natural deduction
Inference schemes
Equivalence schemes
Indirect proof and conditional proof
Exercises
1.9
Logical transformations
Disjunctive normal form
Conjunctive normal form
Exercises
2.
Traditional logic
2.1
Categorical sentences
Subject, predicate, extension of a term
Types of categorical sentences
Alternative ways to form a categorical sentence
Exercises
2.2
Square of opposition.
Exercises
2.3
Immediate inferences
Conversion
Obversion
Contraposition
Exercises
2.4
Syllogisms
What is a syllogism?
Figure and mood
Valid syllogisms
Exercises
2.5
Syllogistic rules
Distribution
Rules
Exercises
2.6
Venn diagrams
Exercises
3.
Predicate logic
3.1
General and singular terms
Exercises
3.2
Variables and quantifiers
Variables, open sentences, existential quantifier
Universal quantifier. Symbolizing categorical sentences
Universe of discourse
Exercises
3.3
The advantages of predicate logic
Differences between traditional and predicate logic
Advantages of predicate over traditional logic
Sentences that traditional logic is unable to symbolize
Exercises
3.4
Syntax and semantics of predicate logic
Syntax of predicate logic
Semantics of predicate logic
3.5
Proof procedure
The relationship between the quantifiers
Universal and existential instantiation
The proof procedure
Properties of relations
Exercises
3.6
Identity
The sign of identity
Definite descriptions
Exercises
3.7
Logical transformations in predicate logic
Rules of passage
Prenex form
Exercises
4.
Non-classical logics
4.1
Modal logic
Modal operators
Syntax of modal logic
Semantics of modal logic
Different kinds of necessity and possibility
Counterfactual conditionals and disposition terms
Exercises
4.2
Three-valued logic
The principle of bivalence and the law of excluded middle
The three-valued logics of Lukasiewicz and Kleene
Other reasons for using three-valued logic
The three-valued logic of Bochvar
Problems in three-valued logic
Exercises
Bibliography
Solutions
Logic
Introduction - logic and logical form
What does logic do?
Logical inference and logical form
Logical words
A brief history of logic
Modern logic
1.
Propositional logic
1.1
Conjunction, negation, disjunction
What does propositional logic do?
Propositions and truth values
Atomic and compound sentences
Conjunction
Negation
Disjunction
Exercises
1.2
Conditional and biconditional
Conditional
Biconditional
A systematic way to symbolize natural language sentences
Exercises
1.3
Truth tables
Syntax of propositional logic
Semantics of propositional logic. Truth tables
Exercises
1.4
Indirect proof
Exercises
1.5
Truth-value analysis
Exercises
1.6
Logical inference and logical equivalence
Logical inference
Logical equivalence
Exercises
1.7
Quick test of logical inference
Exercises
1.8
Natural deduction
Inference schemes
Equivalence schemes
Indirect proof and conditional proof
Exercises
1.9
Logical transformations
Disjunctive normal form
Conjunctive normal form
Exercises
2.
Traditional logic
2.1
Categorical sentences
Subject, predicate, extension of а term
Тypes of categorical sentences
Alternative ways to form a categorical sentence
Exercises
2.2
Square of opposition
Exercises
2.3
Immediate inferences
Conversion
Obversion
Contraposition
Exercises
2.4
Syllogisms
What is a syllogism?
Figure and mood
Valid syllogisms
Exercises
2.5
Syllogistic rules
Distribution
Rules
Exercises
2.6
Venn diagrams
Exercises
3.
Predicate logic
3.1
General and singular terms
Exercises
3.2
Variables and quantifiers
Variables, open sentences, existential quantifier
Universal quantifier. Symbolizing categorical sentences
Universe of discourse
Exercises
3.3
The advantages of predicate logic
Differences between traditional and predicate logic
Advantages of predicate over traditional logic
Sentences that traditional logic is unable to symbolize
Exercises
3.4
Syntax and semantics of predicate logic
Syntax of predicate logic
Semantics of predicate logic
3.5
Proof procedure
The relationship between the quantifiers
Universal and existential instantiation
The proof procedure
Properties of relations
Exercises
3.6
Identity
The sign of identity
Definite descriptions
Exercises
3.7
Logical transformations in predicate logic
Rules of passage
Prenex form
Exercises
4.
Non-classical logics
4.1
Modal logic
Modal operators
Syntax of modal logic
Semantics of modal logic
Different kinds of necessity and possibility
Counterfactual conditionals and disposition terms
Exercises
4.2
Three-valued logic
The principle of bivalence and the law of excluded middle
The three-valued logics of Lukasiewicz and Kleene
Other reasons for using three-valued logic
The three-valued logic of Bochvar
Problems in three-valued logic
Exercises
Bibliography
Solutions
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