Formation rule
In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language.[1] These rules only address the location and manipulation of the strings of the language. It does not describe anything else about a language, such as its semantics (i.e. what the strings mean). (See also formal grammar).
if we take Φ to be a propositional formula we can also take Φ to be a formula;
if we take Φ and Ψ to be a propositional formulas we can also take (Φ Ψ), (Φ Ψ), (Φ Ψ) and (Φ Ψ) to also be formulas.
The formation rules of a propositional calculus may, for instance, take a form such that;
A predicate calculus will usually include all the same rules as a propositional calculus, with the addition of quantifiers such that if we take Φ to be a formula of propositional logic and α as a variable then we can take (α)Φ and (α)Φ each to be formulas of our predicate calculus.
