Akademik

(pl. schemata)

In many logical calculi, axioms and rules are presented as forms or schemata, with the provision that any of an infinite number of substitution instances are axioms. For example, the rule of inference modus ponens may be presented as A; A → B, so B, where A and B can be substituted by any well-formed formula of the calculus. Statements that are intuitively framed by talking of all functions, all properties, etc., such as Peano's fifth postulate, or the set-theoretic axioms of separation and replacement, are represented by axiom schemata in first-order logic.