Metalogic is a branch of propositional logic, which addresses problems of epistemology in the tradition of Analytic Philosophy. The meta in metalogic, as usual, indicates a self-referential quality. Metalogic is the use of analytic proof to determine the properties of a system of propositional logic.
Metalogical proofs usually resemble a hybrid of mathematical and propositional proofs. Godel's theorem is one of the most famous metalogical proofs.
The ultimate goal of metalogical investigation is to determine whether a system of propositional logic is both consistent (meaning no false statements can be proven true) and complete (meaning all true statements can be proven true).