Editing Metalogic (section)

{{short description|Study of the properties of logical systems}}
'''Metalogic''' is the [[metatheory]] of [[logic]]. Whereas ''logic'' studies how [[formal system|logical system]]s can be used to construct [[Validity (logic)|valid]] and [[soundness|sound]] [[argument]]s, metalogic studies the properties of [[Logical system|logical systems]].<ref>Harry Gensler, [https://books.google.com/books?id=jpteBwAAQBAJ Introduction to Logic], Routledge, 2001, p. 336.</ref> Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived ''about'' the [[formal language|languages]] and systems that are used to express truths.<ref name="metalogic">{{Hunter 1996}}</ref>

The basic objects of metalogical study are formal languages, formal systems, and their [[Interpretation (logic)|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 system]]s is the branch that is known as [[proof theory]].