linguistic:paraphrasing
Categorial grammar

Categorial grammar is an approach in which constituents combine as function and argument, according to combinatory possibilities specified in their syntactic categories. For example, other approaches might posit a rule that combines a noun phrase (NP) and a verb phrase (VP), but CG would posit a syntactic category NP and another NP\S, read as "a category that searches to the left (indicated by \) for an NP (the element on the left) and outputs a sentence (the element on the right)." Thus, the syntactic category for an intransitive verb is a complex formula representing the fact that the verb acts as a function word requiring an NP as an input and produces a sentence level structure as an output. The complex category is notated as (NP\S) instead of V. The category of transitive verb is defined as an element that requires two NPs (its subject and its direct object) to form a sentence. That is notated as (NP/(NP\S)), which means, "A category that searches to the right (indicated by /) for an NP (the object) and generates a function (equivalent to the VP) which is (NP\S), which in turn represents a function that searches to the left for an NP and produces a sentence."

Tree-adjoining grammar is a categorial grammar that adds in partial tree structures to the categories.