\begin{definition}[Definition:Formal Grammar/Bottom-Up]
Let $\LL$ be a formal language whose alphabet is $\AA$.
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A '''bottom-up grammar''' for $\LL$ 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 complex situations, for example in the bottom-up specification of predicate logic
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  |section = tc
  |title = Extremal Clause
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}}
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\end{definition}