Metalogic is the study of the metatheory of logic. While logic is the study of the manner in which logical systems can be used to construct valid and sound arguments, metalogic studies the properties of the logical systems themselves. While logic concerns itself with the truths that may be derived using a logical system, metalogic concerns itself with the truths which may be derived about the languages, and systems that are used to express truths.
The basic objects of study in metalogic are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic known as model theory, while the study of deductive systems is the branch known as proof theory.
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