Wiktionary
n. (context philosophy English) The metatheory of logic; the study of property of logical systems.
Wikipedia
Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.
The basic objects of metalogical study are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory, and the study of deductive systems is the branch that is known as proof theory.
Usage examples of "metalogic".
The metalogic of solving puzzles is a good deal more complex than the logic of then-solutions.