<?xml version="1.0" standalone="yes"?>
<Paper uid="W06-1506">
  <Title>Pied-Piping in Relative Clauses: Syntax and Compositional Semantics based on Synchronous Tree Adjoining Grammar</Title>
  <Section position="4" start_page="0" end_page="42" type="metho">
    <SectionTitle>
2 STAG-based Compositional Semantics
</SectionTitle>
    <Paragraph position="0"> Before presenting my analysis of relative clauses, I first illustrate the framework of STAG-based compositional semantics and clarify my assumptions, using a simple sentence that contains an existential quantifier and an attributive adjective in (3).</Paragraph>
    <Paragraph position="1"> (3) John saw a good movie.</Paragraph>
    <Paragraph position="2"> I use STAG as defined in Shieber (1994). In an STAG, each syntactic elementary tree is paired with one or more semantic trees that represent its logical form with links between matching nodes.</Paragraph>
    <Paragraph position="3"> A synchronous derivation proceeds by mapping a derivation tree from the syntax side to an isomorphic derivation tree in the semantics side, and is synchronized by the links specified in the elementary tree pairs. In the tree pairs given in Figure 1, the trees in the left side are syntactic elementary trees and the ones in the right side are semantic trees. In the semantic trees, F stands for formulas, R for predicates and T for terms. I assume that these nodes are typed and I represent predicates as unreduced l-expressions. The linked nodes are shown with boxed numbers. For sake of simplicity, in the elementary tree pairs, I only include links that are relevant for the derivation of given examples.</Paragraph>
    <Paragraph position="4"> Figure 1 contains elementary trees required to generate the syntactic structure and the logical  gle lexical head&amp;quot; (Frank 2002, p. 54). Particularly, (aa movie) is a valid elementary tree, as a noun can form an extended projection with a DP, in line with the DP Hypothesis. The proper name tree in (aJohn) is paired with a tree representing a term in the semantics, and the attributive adjective tree in (bgood) is paired with an auxiliary tree in the semantics that represents a one-place predicate to be adjoined to another one-place predicate. As for the syntax-semantics pairing of elementary trees for quantified DPs, I follow Shieber and Schabes (1990), and use Tree Local Multi-Component TAG (as defined in Weir (1988)) in the semantics. Thus, the DP in (aa movie) is paired with a multi-component set {(aprimea movie), (bprimea movie)} in the semantics: (aprimea movie) provides an argument variable, and (bprimea movie) provides the existential quantifier with the restriction and scope. The transitive tree in (asaw) is paired with a semantic tree representing a formula that consists of a two-place predicate and two term nodes. The links, shown with boxed numbers, guarantee that whatever substitutes into DPi, the corresponding semantic tree will substitute into the term node marked with 1 , and whatever substitutes into DP is paired up with a multi-component set in the semantics where one of the components will substitute into the term node marked with 2 and the other will adjoin onto the F node marked with 2 . The syntactic and semantic derivation trees are given in Figure 2, and the derived trees are given in Figure 3. I leave out the tree addresses in the semantic derivation tree, as these are determined by the links between the syntactic and se- null The semantic derived trees can be reduced by applying l-conversion, as the nodes dominate typed l-expressions and terms. When reducing semantic derived trees, in addition to l-conversion, I propose to use Predicate Modification, as defined in Heim and Kratzer (1998) in (4).</Paragraph>
    <Paragraph position="5">  sume multiple adjoining (as defined in Schabes and Shieber (1994)) of quantifier trees at the same F node, leaving the order unspecified. This provides an underspecified representation and accounts for scope ambiguity.</Paragraph>
    <Paragraph position="6">  and [[b]]s and [[g]]s are both in D&lt;e,t&gt;, then [[a]]s = lxe[[b]]s(x) [?] [[g]]s(x).</Paragraph>
    <Paragraph position="7"> The application of Predicate Modification and l-conversion to (gprime3) reduces it to the formula in (5). (5) [?]x[good(x) [?] movie(x)] [saw(Johnprime,x)]</Paragraph>
  </Section>
  <Section position="5" start_page="42" end_page="44" type="metho">
    <SectionTitle>
3 An STAG analysis of pied-piping in
</SectionTitle>
    <Paragraph position="0"> relative clauses I propose the elementary tree pairs in Figure 4 for the syntactic derivation and semantic composition of the relative clause in (1). In the syntax side, (awho) substitutes into DPj in (bhit), and the pied-piping of the rest of the DP is achieved by adjoining (b's brother) onto (awho). The tree in (b's brother) is a widely-accepted genitive structure according to the DP hypothesis, where the genitive 's heads the DP tree. This satisfies CETM, as a DP is an extended projection of a noun. Substituting (amary) into DPi in (bhit) completes the derivation of the relative clause.</Paragraph>
    <Paragraph position="1"> The derivation tree for the relative clause is in (d1) in Figure 5 and the derived tree is in (g1) in  hit Semantically, we must make sure that the variable coming from the wh-word is also the one being predicated of the head noun (boy in (1)), and yet the same variable does not serve as an argument of the predicate (hit in (1)) in the relative clause. I argue that the introduction of a generalized quantifier (GQ) node in the semantic tree in (bprimewho) and adjoining of (bprime's brother) onto the GQ node guarantee this. I define the logical form of a wh relative pronoun as an auxiliary tree given in (bprimewho). In (bprimewho), lx binds x in the generalized quantifier, lP.P(x). Adjoining (bprimewho) onto the relative clause elementary tree in (bprimehit) essentially has the effect of abstracting over the variable coming from the wh-word in the relative clause, turning it into a one-place predicate. This therefore ensures that the relative clause and the head noun are predicating over the same variable, deriving the interpretation of the relative clause as a modifier of the head noun. The meaning of the pied-piped material 's brother is added onto the meaning of who by adjoining the auxiliary tree defined in (bprime's brother) onto the GQ node in (bprimewho). In (bprime's brother), ly ensures that the variable coming from the DP* (who) is in some relation with the variable coming from the head of the pied-piped DP (whose brother), and lQ, by turning whose brother into a GQ, ensures that the variable coming from the head of the pied-piped DP is the argument of the predicate that the DP combines with. The derivation tree and the derived tree in the semantics side are given in (dprime1) in Figure 5 and (gprime1) in Figure 6. After all the l-conversions have applied, (gprime1) can be reduced to the expression in (6).</Paragraph>
    <Paragraph position="2">  The expression in (6) is a one-place predicate which can be paraphrased as a set of all x's such that there is a unique brother z and x is in some relation with z and Mary hit z. As the semantics of relative clauses is defined to be a one-place predicate, it is analogous to attributive adjectives. This means that the semantic tree resulting from the adjoining of (gprime1) onto the logical form of the head noun boy can be reduced to the expression in</Paragraph>
    <Paragraph position="4"> The derivation of a sentence containing (1), a boy whose brother Mary hit, as the object, as in (8), proceeds in a similar fashion as in (3), yielding the semantic derived tree which is reducible to the formula in (9).</Paragraph>
    <Paragraph position="5">  For the syntactic derivation and the compositional semantics of the relative clause in (2), all we need to do is add the tree pair in Figure 7 to the set of elementary tree pairs in Figure 4. In the syntax side, (b's friend) adjoins onto (b's brother) and in the semantics side, (bprime's friend) adjoins onto (bprime's brother), as shown in the derivation trees in  The semantic derived tree (gprime2) can be reduced to the expression in (10) through l-conversions.angbracketleftbigg</Paragraph>
  </Section>
  <Section position="6" start_page="44" end_page="46" type="metho">
    <SectionTitle>
4 Extensions
</SectionTitle>
    <Paragraph position="0"> The proposed syntax and the semantics of pied-piping can straightforwardly be extended to cases in which the wh-word is embedded in a PP, as in (11).</Paragraph>
    <Paragraph position="1"> (11) a boy [ [DP the brother of whom]i Mary hit ti ] For the derivation of (11), we need to change two of the elementary tree pairs in Figure 4 slightly. The elementary tree pairs &lt;(awho), (bprimewho)&gt; and &lt;(b's brother), bprime's brother)&gt; need to be replaced with the pairs in Figure 10. Since the relative pronoun in (11) is whom, we use a DP tree anchoring whom in (awhom). The corresponding semantic tree (bprimewhom) remains exactly the same as before. (bthe brother of) represents the pied-piped material in DP. It is a well-formed elementary tree according to CETM as it has a single lexical head brother and DP is an extended projection of this head, and PP is not subject to CETM because P is a functional head, not a lexical head. Moreover, DP* is licensed as it is an argument of the lexical head brother, as argued in Kroch (1989). The semantics of the brother of whom is equivalent to whose brother, and therefore, we pair up (bthe brother of) with the exact same semantic tree as (bprime's brother).</Paragraph>
    <Paragraph position="2"> The derivation trees for the relative clause in (11) are given in Figure 11. They look exactly the same as the ones for the relative clause in (1), except for names of the elementary trees in a few nodes. The derived trees are given in Figure 12.</Paragraph>
    <Paragraph position="3"> While the syntactic derived tree (g11) is different from (g1) in Figure 6 in the structure of DP containing the pied-piped material, the semantic derived tree (gprime11) looks exactly the same as (gprime1) in Figure 6. This is as it should be given that the meaning of (1) and the meaning of (11) are equivalent. null  brother of The proposed analysis can also be extended to relative clauses in which no pied-piping has taken place. When the larger DP containing the relative pronoun is indefinite or non-specific, the DP can be stranded, as in (12). This gives us a configuration where a wh-word has extracted out of a DP. (12) a boy [whomi Mary hit [DP a brother of ti]] Since we now have a DP with an indefinite article, a tree pair in Figure 13 is needed, for the derivation of (12). Using the semantic tree (bprimea brother of), the semantic composition of the relative clause in (12) can proceed as before: the semantic tree (bprimea brother of) adjoins onto the semantic tree (bprimewhom) in Figure 10, which then adjoins onto (bprimehit) in Figure 4. In the syntax, however, we must make sure that (ba brother of) does not adjoin onto the relative pronoun whom, because if it did, we would end up with the string a brother of whom. Instead, what we need is for (ba brother of) to adjoin onto the DP dominating the trace of the extracted object in (bhit). This however is not a valid derivation in STAG, as elementary trees in a single pair are composing with two trees from two different pairs. A slight modification in the syntactic elementary tree for (awhom) in Figure 14 can fix this problem. I propose to do this by turning (awhom) into a multi-component set {(awhom), (bwhom)} as in Figure 14. An auxiliary tree like (bwhom), which  brother of does not dominate any other nodes, is a degenerate tree, and has been used in Kroch (1989) and Frank (2002) to handle extraction from a wh-island, as in [Which car]i does Sally wonder how to fix ti? In syntax, to derive the relative clause in (12), (awhom) substitutes into DPj in (bhit) as before, and (bwhom) adjoins onto the DP dominating the trace of the extracted object in (bhit), as shown in the derivation tree (d12) in Figure 15. And in semantics, (bprimewhom) adjoins onto (bprimehit) as before, as shown in (dprime12) in Figure 15. Subsequently, in syntax (ba brother of) adjoins onto (bwhom) giving us the DP a brother of tj, and in semantics (bprimea brother of) adjoins onto (bprimewhom). Thus, by using the multi-component set {(awhom), (bwhom)}, we now have a situation where two elementary trees in a single pair are composing with two trees belonging to another pair. The syntactic and the semantic derived trees are given in Figure 16. After l-conversions, (gprime12) can be reduced to the expression in (13).2</Paragraph>
  </Section>
class="xml-element"></Paper>