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metalogic
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.〔Harry Gensler, Introduction to Logic, Routledge, 2001, p. 253.〕 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.〔Hunter, Geoffrey, ''Metalogic: An Introduction to the Metatheory of Standard First-Order Logic'', University of California Press, 1971〕
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.
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