Structural relations 1 Basic definitions

In this theory, phrase structure is fully determined by the phrase structure sets that contain treelets, and by the dominance relations encoded within each treelet. Given these prim itives and the notion o f dominance in (29) above, the derived relation o f immediate dominance can be defined over head categories of treelets as follows.

(3 8 )X immediately dominates Y if X and Y are head categories o f distinct treelets and X dominates Y and there is no category Z distinct from X and Y such that X dominates Z and Z dominates Y.

S om e c o n seq u en ces o f the d iscu ssion o f the trees in (30a) and (31) for the an a ly sis o f verb m ovem en t and o f the d isc u ssio n o f the tree in (3 4 ) for “ X P ” m ovem ent w ill be discussed shortly.

It should be noted that, since immediate dominance is a derived notion, the phrase structure sets contain no separate statement of immediate dom inance relations. Among other things, this m eans that there can be no two phrase structure sets that are distinguished only by their imm ediate dominance relations.^^

Given the derived notion o f immediate dominance, the usual structural relations can be defined as follows:

(39) a. X is the DAUGHTER o f Y, if Y immediately dominates X. b. Y is the MOTHER o f X, if Y immediately dominates X.

c . X a n d Y a re s i s t e r s i f t h e y are d is tin c t an d h a v e th e s a m e m o t h e r . M oreover:

(40) a. X is the ROOT o f the structure if it is not dominated by a distinct category. b. X is a TERMINAL i f it d o e s n o t d o m in a te a n y o th er c a t e g o r ie s .

c. X and Y are c o n n e c t e d if X is dominated by Y or Y is dom inated by X.

The assumptions o f the present proposal require a slight reform ulation o f the c- command relation (cf. Reinhart 1976). Since the rejection o f categorial projection allows lexical heads to dom inate other categories, there is no reason to exclude a category from c- comm anding categories that it dominates. The relation can then be form ulated as follows: (41) X C-COMMANDS Y iff there is no category Z such that Z imm ediately dominates X

and Z does not dom inate Y.

Phrase structure sets can then be constrained by the following conditions (cf. Partee et al 1990:437-441 on properties o f tree diagrams).

(42) Si n g l e Ro o t Co n d i t i o n: There is exactly one treelet whose dom inance set contains all the categories contained in the phrase structure set.

(43) Bi n a r y Br a n c h i n g: Each category has at most two daughters.

T his is the reason w h y the tree structures in (3 0 ) and (31) collapse to a sin g le phrase structure set.

Note that the Single Root Condition implies that every category is connected to the root. It should be noted that while the above notions can all be defined within the model proposed here, it is not necessarily the case that all of them actually have a linguistic reality. The effects o f some o f them may turn out to be derivable from m ore primitive notions, while others may turn out to be empirically unfounded. A case o f the former is the notion o f c-com mand, which has been derived (or, in one case, eliminated) in different ways in Brody 1997a, 2000, Epstein et al 1998, Neeleman and van de Koot 2002. A case o f the latter is the Single Root Condition, which Chametzky 1995 argues against. Since these considerations have no direct bearing on the issues discussed here, I will continue to use these standard notions in order not to detract from innovations in other places.

4.3.2 Specifiers and complem ents

N ow we can turn to the distinction between specifiers and c o m p le m e n ts .I assume, as in standard X -bar theory, that each head is related to at most two dependents, namely a single specifier/adjunct and a single complement (cf. also Kayne 1994, Cinque 1999, contra Chom sky 1995b). Unlike in conventional approaches, however, it is not possible in the present theory to distinguish structurally a specifier from a complement. Thus, while in a conventional structure, the complement is sister to a head and the specifier sister to the first projection o f the head, in the model without categorial projection developed here, both specifier and com plem ent are daughters to the head;

(44) a. X -bar structure: XP / \ Spec X ’ / \ X Comp b. ‘Telescope’ structure X / \ Spec Comp

I am grateful to K lau s A b els for d iscu ssion o f thi^ issue. He proposed a different approach to the sp ec ifier/co m p lem e n t distin ction in terms their different status with regard to the functional sequ en ce in cla sse s at the e g g sch o o l in N o v i Sad 20 0 2 .

N evertheless, the complement o f a head can be identified through reference to e x t e n d e d PROJECTIONS ( c f Grim shaw 1991). It has long been recognised that verbs and nouns are related to different functional categories. Thus, e.g. tense and com plementizers go with verbs, while determiners go with nouns. A verb is said to form an extended projection with the functional categories to which it is related. In the present proposal, a (non-derived) lexical verb then forms an extended projection with all its derived heads and with associated functional heads such as auxiliaries and complementizers."^' Intuitively, the complement o f a branching category Z is then that daughter o f Z that is part o f the same extended projection.