Disjunctive syllogism

The mode tollendo ponens or disjunctive syllogism is a final figure of the classical propositional logic and a rule of inference many logical calculi, which allows a set of the form A or B and a set of the form of non- A to infer a set of the form B. It is so - spoken content - from the knowledge that at least one of two situations must exist, but that one of the two does not exist, concluded that the other must be of the two.

The Latin name mode tollendo ponens, free " of inference (modus ), by rejecting [ denial ] ( tollendo ) [ a statement ] a [ other ] statement is [ derived ] ( ponens ) ", explained by the fact that at a given first premise, A ∨ B, by the negation (¬ a) a statement is another statement B, " set " ( derived ).

Since a set A ∨ B is also called disjunction, referred to the tollendo modus ponens sometimes called " disjunctive syllogism ".

Formulation

From the premises

Follows the conclusion

Evidence

The logical equivalence of the statements A ∨ B and ¬ A → B follows from the definitions of disjunction, and negation subjunction.

Left side:

Right side: