A valid form of logical inference in propositional logic, which infers from two conditional and a disjunct statement a new disjunct statement.
Formally, the constructive dilemma has three premises, it looks as follows:
Premise 1:A → B– (if A, then B)
Premise 2:C → D– (if C, then D)
Premise 3:A ∨ C– (A or C)
Conclusion:B ∨ D– (B or D)
The constructive dilemma can be seen as a combination of two Modus Ponens which are connected by a disjunct statement.
The term “dilemma” in this context should be understood as a “decision” between two conditionals.
An example for a constructive dilemma could be:
If the sun shines tomorrow, [then] we will go to the beach.
If it rains tomorrow, [then] we will go to the museum.
Tomorrow the sun will shine, or it will rain [or both].
Therefore we will tomorrow go to the museum or to the beach [or both].