Intuitionistic logic, sometimes more generally called
constructive logic, is a system of
symbolic logic that differs from
classical logic by replacing the traditional concept of truth with the concept of
constructive provability. For example, in classical logic,
propositional formulae are always assigned a
truth value from the two element set of trivial
propositions ("true" and "false" respectively) regardless of whether we have direct
evidence for either case. In contrast, propositional formulae in intuitionistic logic are
not assigned any definite truth value at all and instead
only considered "true" when we have direct evidence, hence
proof. (We can also say, instead of the propositional formula being "true" due to direct evidence, that it is
inhabited by a proof in the
Curry–Howard sense.) Operations in intuitionistic logic therefore preserve
justification, with respect to evidence and provability, rather than truth-valuation.