Intermediate logic

In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. A logic is a set of propositional formulas with certain closure properties. The logics are partially ordered under containment. A logic is stronger than another iff it contains the other.

Classical logic is the strongest consistent superintuitionistic logic. Thus, the consistent superintuitionistic logics are called intermediate logics, because the logics are intermediate in how many formulas they contain between intuitionistic logic and classical logic.