Constructive dilemma[1][2][3] is a
validrule of inference of
propositional logic. It is the
inference that, if P implies Q and R implies S and either P or R is true, then either Q or S has to be true. In sum, if two
conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too. Constructive dilemma is the
disjunctive version of
modus ponens, whereas,
destructive dilemma is the disjunctive version of modus tollens. The constructive dilemma rule can be stated:
where the rule is that whenever instances of "", "", and "" appear on lines of a proof, "" can be placed on a subsequent line.
Formal notation
The constructive dilemma rule may be written in
sequent notation: