Rules of Interference (KR 1.6)

• Basic Rules of Inference
• Quantified Rules of Inference

3 Categories of Compound Propositions

Tautology: regardless of truth values of the individual, constituent propositions, the compound proposition is always true

Contradiction: regardless of truth values of the individual, constituent propositions, the compound proposition is always false

Contingency: the compound proposition is true for some values of the constituent propositions, and false for the other values of the constituent propositions

Arguments

an argument is a sequence of statements that ends with a conclusion and for which the preceding statements are called premises

an argument is valid if and only if it is impossible for all premises to be true and the conclusion to be false

• Notation:

Common Tautologies

• Modus Ponens (affirming)
• Universal Modus Ponens
• Modus Tollens (disproving)
• Hypothetical Syllogism (p→q→r)
• Disjunctive Syllogism
• Addition
• Simplificaion
• Conjunction