metalogical
Adjective
Meaning
Beyond the scope or province of logic.
Source: Webster's dictionaryExamples
The cost of this expressiveness is that second-order and higher-order logics have fewer attractive metalogical properties than first-order logic.
Judgments can have material, formal, transcendental, or metalogical truth.
Lindström's theorem main Per Lindström showed that the metalogical properties just discussed actually characterize first-order logic in the sense that no stronger logic can also have those properties (Ebbinghaus and Flum 1994, Chapter XIII).
Restrictions such as these are useful as a technique to reduce the number of inference rules or axiom schemas in deductive systems, which leads to shorter proofs of metalogical results.
The rules are: : and : where " " is a metalogical symbol representing "can be replaced in a proof with."