Constructive logic

Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “we can construct”. In order to work constructively, we need to re-interpret not only the existential quantifier but all the logical connectives and quantifiers as instructions on how to construct a proof of the statement involving these logical expressions. (…) To summarise: to prove ¬p, we may, and normally do, assume p and derive a contradiction. To prove p, it is not enough to assume ¬p and derive a contradiction.

One aspect is that the law of excluded middle is not admitted, but it is much more than that.

Another word for it is Intuitionistic, cf martin-lofIntuitionisticTypeTheory1984