Dependency grammar (DG) is a class of modern grammatical theories that are all based on the dependency relation (as opposed to the constituency relation of phrase structure) and that can be traced back primarily to the work of Lucien Tesnière. Dependency is the notion that linguistic units, e.g. words, are connected to each other by directed links. The (finite) verb is taken to be the structural center of clause structure. All other syntactic units (words) are either directly or indirectly connected to the verb in terms of the directed links, which are called dependencies. Dependency grammar differs from phrase structure grammar in that while it can identify phrases it tends to overlook phrasal nodes. A dependency structure is determined by the relation between a word (a head) and its dependents. Dependency structures are flatter than phrase structures in part because they lack a finite verb phrase constituent, and they are thus well suited for the analysis of languages with free word order, such as Czech or Warlpiri. The notion of dependencies between grammatical units has existed since the earliest recorded grammars, e.g. Pāṇini, and the dependency concept therefore arguably predates that of phrase structure by many centuries. Ibn Maḍāʾ, a 12th-century linguist from Córdoba, Andalusia, may have been the first grammarian to use the term dependency in the grammatical sense that we use it today. In early modern times, the dependency concept seems to have coexisted side by side with that of phrase structure, the latter having entered Latin, French, English and other grammars from the widespread study of term logic of antiquity. Dependency is also concretely present in the works of Sámuel Brassai (1800–1897), a Hungarian linguist, Franz Kern (1830-1894), a German philologist, and of Heimann Hariton Tiktin (1850–1936), a Romanian linguist. Modern dependency grammars, however, begin primarily with the work of Lucien Tesnière. Tesnière was a Frenchman, a polyglot, and a professor of linguistics at the universities in Strasbourg and Montpellier.

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Phrase structure grammar
The term phrase structure grammar was originally introduced by Noam Chomsky as the term for grammar studied previously by Emil Post and Axel Thue (Post canonical systems). Some authors, however, reserve the term for more restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars. In a broader sense, phrase structure grammars are also known as constituency grammars. The defining trait of phrase structure grammars is thus their adherence to the constituency relation, as opposed to the dependency relation of dependency grammars.
Head-driven phrase structure grammar
Head-driven phrase structure grammar (HPSG) is a highly lexicalized, constraint-based grammar developed by Carl Pollard and Ivan Sag. It is a type of phrase structure grammar, as opposed to a dependency grammar, and it is the immediate successor to generalized phrase structure grammar. HPSG draws from other fields such as computer science (data type theory and knowledge representation) and uses Ferdinand de Saussure's notion of the sign. It uses a uniform formalism and is organized in a modular way which makes it attractive for natural language processing.
Adjunct (grammar)
In linguistics, an adjunct is an optional, or structurally dispensable, part of a sentence, clause, or phrase that, if removed or discarded, will not structurally affect the remainder of the sentence. Example: In the sentence John helped Bill in Central Park, the phrase in Central Park is an adjunct. A more detailed definition of the adjunct emphasizes its attribute as a modifying form, word, or phrase that depends on another form, word, or phrase, being an element of clause structure with adverbial function.
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