Modus ponendo tollens

The mode ponendo tollens is a final figure of the classical propositional logic and a rule of inference many logical calculi, which permits a sentence of the form not (A and B) and a set of the form A not B to infer a set of the form:

From the premises

Follows the conclusion

It is so - spoken content - from the knowledge that two particular substance can not exist simultaneously, but that one of the two situations is very well concluded that the other of the two does not exist.

The Latin name mode ponendo tollens, free " of inference (modus ) that by setting ( ponendo ) [ a statement ] rejects an [ other ] statement ( tollens ), explained by the fact that, given the first premise, ¬ (A ∧ B) "rejected " by setting a second, positive (non- United ) premise, A, a statement, B (no) is.

Evidence

The logical equivalence of the statements ¬ (A ∧ B) and ¬ A → B follows from the definitions of conjunction, subjunction and the negation.

Left side:

Right side: