Double negative elimination

The law of double negation (also principle of double negation, or Latin duplex negatio affirmat - reaffirms the double negative / yes) is a law of classical logic according to which the denial of a negated ( declarative ) sentence is its affirmation, a double verne inter- sentence ¬ ¬ A that is the same truth- value as the non- unified set A.

The double negation in the sense of logic is to be distinguished from the negation of the negation in the sense of the dialectic ( Hegel ).

The validity of the law of double negation is fully in classical logic, since there the bivalence applies. In intuitionistic logic, the law is not valid. This only A → ¬ ¬ A but not ¬ ¬ A → A. applies

As a final rules could be given with the double negation introduction and the double negation elimination.

The rule of double negation introduction says that if A can be inferred from a set of assumptions X of the set, then it can be inferred from the same set X, the double negation of A, ie ¬ ¬ A.

The rule of double - negation elimination says that if one of a set of assumptions X is the double negation of A - can deduce, therefore ¬ ¬ A, then one can conclude from this set X is also on A.

Whether a double negative in a natural language is the first negation cancels ( German, Latin ), or enhanced ( French, Spanish ), depends on the language.

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• Logic