Theta-roles and checking

Z X S T Y

4.1.4

Theta-roles and checking

MG distinguishes betweenargumentsandadjuncts. Arguments are constituents that are obligatory for the grammaticality of a sentence (e.g. (4.11) is grammat- ical, but (4.12) is not, because the argument ‘Edward’ is missing). Adjuncts are optional: they can be left out without influencing the grammaticality of the sentence (e.g. both (4.11) and (4.13) are grammatical, even though the adjunct ‘every day’ is left out in (4.11)).

(4.11) Bella loves Edward. (4.12) * Bella loves.

(4.13) Bella loves Edward every day.

We say that predicates subcategorize for certain kinds of expressions. These expressions can be of different semantic types. For example, in (4.14) the predi- cate (‘give’) subcategorizes for an Agent (something that initiates the action, in casu ‘Bella’), a Theme (something that undergoes the action, in casu ‘the book’) and a Goal (something towards which the action is oriented, in casu ‘Edward’). Agent, Theme and Goal (among others) are calledthematic roles orθ-roles. (4.14) Bella gives the book to Edward

So a predicate assignsθ-roles to constituents in a sentence. More specifically, a predicate has to assign eachθ-role it has to a constituent in a sentence, other- wise the sentence is ungrammatical (e.g. (4.12) is ungrammatical, because the predicate’s Theme-role is not assigned). Moreover, each constituent in the sen- tence can only be assigned oneθ-role (e.g. we cannot say that in (4.12) ‘Bella’ is both the Agent and the Theme, meaning that she loves herself). These two observations taken together constitute the Uniqueθ-Generalization:

Uniqueθ-Generalization eachθ-role must be assigned but a constituent can- not be assigned more than oneθ-role (Adger, 2003, p. 81)

The apparatus to enforce this generalization consists of categorial selectional features (c-selectional features).

C-selectional features a c-selectional feature is a categorial feature on a lex- ical item, which does not determine the distribution of the lexical item itself; rather it determines the category of the elements which will be able to Merge with that lexical item

For example, the predicate ‘love’ carries two c-selectional features, [uN,uN],3in- dicating that it can Merge with two items which have themselves the categorial feature [N] (indicating that they are nouns). Recall the distinction made above between interpretable and uninterpretable features. Clearly, these c-selectional features have a purely syntactic function and are thus uninterpretable. There- fore, we mark them with au, to distinguish them from the interpretable cate- gorial features. Above we mentioned the principle of Full Interpretation: unin- terpretable features must be deleted before LF. Now we have all the machinery in place to establish this.

We have the following two principles:

3_{Recall thatuin front of a feature indicates that it is uninterpretable. So the ‘N’-feature}

on ‘love’ is uninterpretable, because it indicates which category of elements will be able to Merge with ‘love’, but the ‘N’-feature on ‘Edward’ is interpretable, because it indicates the category of ‘Edward’ itself.

Checking Requirement uninterpretable (c-selectional) features must be checked, and once checked, they can delete

Checking under Sisterhood an uninterpretable c-selectional feature F on a syntactic object Y is checked when Y is sister to another syntactic object Z which bears a matching feature F

Suppose we have the following tree: X Y[uF] Z[F]

Y has an uninterpretable feature F, which needs to be checked according to the Checking Requirement. Z bears a matching feature F, and is in a sisterhood relation with Y, so by Checking under Sisterhood Y’s [uF] can be checked:

X Y[uF] Z[F]

At the point where LF will be produced, all checked features will delete, and Full Interpretation will be satisfied.

A more concrete example is the following. Suppose we have the lexical items

love[V,uN] andEdward[N]. We can Merge these two items and get VP

love[V,uN] Edward[N]

Now we can check the uninterpretable uN-feature and get VP

love[V,uN] Edward[N]

Note that we need a constituent with a matching feature for all c-selectional features on a predicate. The link with the Uniqueθ-Generalization is now fairly straightforward: eachθ-role is associated with a c-selectional feature and hence, eachθ-role will be associated with a constituent in the sentence. A remaining problem is how to determine which constituent gets whichθ-role; this is called theLinking Problem and will be dealt with in Subsection 4.2.1.

Now we see that Merge is triggered by feature checking: we need to Merge with other constituents to be able to check uninterpretable features. Then we have the following definition of Merge:

Merge 1. Merge applies to two syntactic objects to form a new syntactic object

2. the new syntactic object is said to contain the original syntactic ob- jects, which are sisters but which are not linearized

4. Merge allows the checking of an uninterpretable c-selectional feature on a head, since it creates a sisterhood syntactic relation

(Adger, 2003, p. 90–91)

This is the most specific definition given in Adger (2003). When we look at Chomsky (1995), the definition proposed there is not much clearer:

Applied to two objects α and β, Merge forms the new object K, eliminatingαandβ [. . .] K must be constituted somehow from the items αand β [. . .] The simplest object constructed from α and β

is the set{α,β}, so we take K to involve at least this set, whereα

andβ are theconstituents of K [. . .] K must therefore at least (and we assume at most) be of the form {γ, {α, β}}, where γ identifies the type to which K belongs, indicating its relevant properties. Call

γ thelabel of K. (Chomsky, 1995, p. 243)

Although both definitions are not mathematically precise, we can gather what is meant. Consider trees as graphs, i.e. tuples (V, E) such thatE⊆V×V, with

E being the set of edges, and V the set of vertices. Now suppose we have two graphs/treesA andB, with α∈ V(A) the root node ofA, and β ∈V(B) the root node ofB. Furthermore, let H be a vertex such that H /∈V(A)∪V(B). Then we define the Merge ofAandB as follows:

Merge_H(A, B) =:M such that

(

V(M) ={H} ∪V(A)∪V(B)

E(M) ={(H, α),(H, β)} ∪E(A)∪E(B)

So ifA andB are trees with headsαand β, thenMerge_H(A, B) is a tree with headH, which containsAandB (and hasαandβ as daughters).

Note that this definition keeps intact the property of Merge to not specify a linear order, i.e. to not distinguish between (4.5) and (4.6).

Now we can defineheads in an independent way:

Head the head is the syntactic object which selects in any Merge operation (Adger, 2003, p. 91)

An important property of heads is that they project: when a head is merged with another constituent, its features are projected to the new syntactic ob- ject. We distinguish betweenminimal, intermediate and maximal projections. The minimal projection is the lexical item itself (designated e.g. ‘N’). When all c-selectional features of a head are satisfied, we call it a maximal projection (des- ignated e.g. ‘NP’). Note that only maximal projections can be merged with other heads (otherwise the unchecked c-selectional features would remain unchecked and the derivation would eventually crash because the Checking Requirement would not be satisfied). With an intermediate or bar-level projection, there are still some c-selectional features to check (designated e.g. ‘N’). The sister of a bar-level projection is called aspecifier.

Now we can say how structures are linearized (recall that Merge doesn’t specify a linear order). In English, heads come to the left of the complements they select; specifiers, however, occur to the left of their head. Adjuncts, finally, can appear either to the left or the right of the phrase they adjoin to.