The hierarchy of clausal functional heads

Cinque matches the order of adverb classes against the order of the clausal functional heads that morphology and scope reveal, and finds the two aligned one to one: each adverb class is the specifier of one head. The result is his universal hierarchy of clausal functional projections, a linear order of heads from the speech-act mood at the top to the lower completive aspect at the bottom. Cartography.Head is that order, its constructors listed bottom-up, each with the adverb class Cinque pairs with it, and Cartography.Head.family reads off the kind of head his label names: a mood, a modality, a tense, an aspect or Voice.

A clause that projects up to a head contains every head below it, so the heads of a clause of size h are the lower set Set.Iic h, and the heads in a clause of size b but not in one of size a form the interval Set.Ioc a b (Set.Iic_sdiff_Iic). A later proposal that adds heads to Cinque's refines the order: its hierarchy receives an order embedding of Cartography.Head, and a head it places immediately above or below one of Cinque's covers it or is covered by it. Cartography.Head.cat sends each head to its category in Minimalist.Cat, and the list Cartography.Head.hierarchy of the heads bottom-up is one of the structures the extension order of Minimalist.Cat is read from. Cinque's own kinds of head are not intervals of the hierarchy: moods, modalities, tenses and aspects interleave.

Main definitions

• Cartography.Head: the heads of the universal hierarchy, with its linear order.
• Cartography.Head.family: the kind of head, Cartography.Family.
• Cartography.Head.cat: the category of a head in Minimalist.Cat.
• Cartography.Head.hierarchy: the heads bottom-up, as a list.

Main statements

• Cartography.Head.mem_hierarchy, Cartography.Head.pairwise_hierarchy: the list holds every head once, in order.
• Cartography.Head.not_isContiguous_family: the kinds of head are not intervals of it.

Implementation notes

• The order is Cinque's second approximation of the hierarchy. His first approximation has a root modal head among the lowest aspects. The second keeps the volitional modal as its only root head, below habitual and the higher repetitive and frequentative aspects, and orders volition above obligation and ability or permission without placing those two among the heads; they are not heads here.
• Cinque marks the pairing of characteristically with generic or progressive aspect, and the head of always, as uncertain.
• Head.cat sends Cinque's four aspect heads below Voice to inner aspect, the aspect of the v shell, the other aspect heads to outer aspect, the speech-act mood to the speech-act head, as Speas and Tenny project their speech-act phrase from Cinque's speech-act mood head, and the other moods but the evidential to Cat.Mood.

References

• Cinque 1999, Adverbs and Functional Heads: A Cross-Linguistic Perspective formalized
• Speas & Tenny 2003, Configurational properties of point of view roles formalized