intuitionistic predicate logic

Intuitionistic predicate logic is a way of reasoning about statements involving objects and properties, emphasizing constructive proof—meaning you can only assert something if you can explicitly demonstrate it. Unlike classical logic, which accepts proofs by contradiction, intuitionistic logic requires that to prove "there exists an object with property P," you must construct or exhibit such an object. This approach avoids assuming truths that can't be explicitly demonstrated, leading to a more cautious and constructive framework for mathematical and logical reasoning.