Definition:Formal Grammar/Bottom-Up

Definition
Let $\mathcal L$ be a formal language whose alphabet is $\mathcal A$.

 A bottom-up grammar for $\mathcal L$ is a formal grammar whose rules of formation allow the user to build well-formed formulas from primitive symbols, in the following way:


 * Letters are well-formed formulas.
 * A collection of specified collations of well-formed formulas, possibly labeled with additional signs, are also well-formed formulas.

In certain use cases, the first clause is adjusted to allow for more more complex situations, for example in the bottom-up specification of predicate logic

Also see

 * Bottom-Up Specification of Propositional Logic
 * Bottom-Up Specification of Predicate Logic