Provability Logic

Provability Logic is a branch of modal logic that formalizes the concept of provability in mathematical systems. It uses modal operators, similar to those expressing possibility and necessity, but focuses on the idea of something being provable. In this context, "necessarily provable" means that a statement can be derived using formal rules, while "possibly provable" indicates that there exists some proof for it. Provability Logic examines the relationships between statements and their provability, exploring how proof interacts with logical systems and revealing insights about consistency and completeness in mathematics.