Derivation Rules
Here are three derivation rules we want to introduce in SA.
- Validity rule: This rule says that if you assume D(n), you can conclude F(n).
- Introspection rule: This rule says that if you have found a legitimate proof for F(n), you can conclude D(n).
- Contradiction rule: This rule says that any formula which leads to a contradiction cannot be derived. This is because, if there is a derivation for the formula, SA will surely contain a contradiction, and then of course, we have nothing to talk about.
See the frame below for exact statements.