Here are some commonly used inference rules
In Propositional Logic
Conditional
- implication introduction
(not to be confused with conditional proofs)
- implication elimination (modus ponens, affirming the antecedent): “If X implies Y, and X is true, then Y is true”
- denying the consequent (modus tollens, denying the consequent): “If X implies Y, and Y is false, then X is false”
Biconditional
- biconditional introduction
- biconditional elimination
and
Conjunction and Disjunction
- conjunction introduction
-
conjunction elimination
and -
disjunction introduction