Link grammar (LG) is a theory of syntax by Davy Temperley and Daniel Sleator which builds relations between pairs of words, rather than constructing constituents in a phrase structure hierarchy. Link grammar is similar to dependency grammar, but dependency grammar includes a head-dependent relationship, whereas link grammar makes the head-dependent relationship optional (links need not indicate direction).[1] Colored Multiplanar Link Grammar (CMLG) is an extension of LG allowing crossing relations between pairs of words.[2] The relationship between words is indicated with link types, thus making the Link grammar closely related to certain categorial grammars.
For example, in a subject–verb–object language like English, the verb would look left to form a subject link, and right to form an object link. Nouns would look right to complete the subject link, or left to complete the object link.
In a subject–object–verb language like Persian, the verb would look left to form an object link, and a more distant left to form a subject link. Nouns would look to the right for both subject and object links.