In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not-P or Q and can replace each other in logical proofs.
Contents
Where "
Formal notation
The material implication rule may be written in sequent notation:
where
or in rule form:
where the rule is that wherever an instance of "
or as the statement of a truth-functional tautology or theorem of propositional logic:
where
Example
An example is:
If it is a bear, then it can swim. Thus, it is not a bear or it can swim.where
If it was found that the bear could not swim, written symbolically as