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<Paper uid="C96-2113">
  <Title>An Underspecified HPSG Representation for Information Structure</Title>
  <Section position="4" start_page="671" end_page="671" type="metho">
    <SectionTitle>
3 An underspecified representation
</SectionTitle>
    <Paragraph position="0"> In computational applications, a compact representation is a prerequisite for any successful treatment of IS. Take the following short sentence with two pitch accents.</Paragraph>
    <Paragraph position="1"> (18) Die Direktorin der Firma MULLER BEGRUSST The director of company Miiller welcomes ihren Besuch.</Paragraph>
    <Paragraph position="2"> her visit/visitors Even if functional elements are ignored, the rules in (12) produce nine alternative F-markings that have to be checked against the context for givenness. In order to resolve the lexical ambiguity of Besueh however (cf. the discussion of (5) above), some partial information about IS suffices. The representation developed here is relatively independent of the underlying semantic theory of focus. Two semantical partitions for focus (FOC) and background (BG) are assumed, each of them a set of semantic conditions. Underspecification is expressed in a graphical way. The interpretation 1deg 9There is some affinity to the f-semantic value in Rooth's (1985) alternative semantics, although the specific details are different.</Paragraph>
    <Paragraph position="3"> rathe interpretation is given informally in the following examples.</Paragraph>
    <Paragraph position="4"> of each syntactic constituent forms a node in tile graph, while the directed edges express accessibility relations.</Paragraph>
  </Section>
  <Section position="5" start_page="671" end_page="671" type="metho">
    <SectionTitle>
BG FOC
</SectionTitle>
    <Paragraph position="0"> The solid line arrows signify obligatory inclusion in the respective IS partition, the dashed line arrows defeasible inclusion. The VP can, e.g., either belong to FOC (via a chain of arrows) or to BG. The graph in (20) represents the amount of information that is encoded on sentence level without reference to context. Additional knowledge may introduce further solid arrows. If, e.g., a begriiflen event is contextually given (like in a question Who greets whom?), the arrow from begriiflt to BG will become an obligatory arrow.</Paragraph>
    <Paragraph position="1"> This arrow again will overrule the dashed arrow from begriiflt to ihren Besuch. Since the latter was the only path to access the FOC partition, the complete graph will collapse into a fully specified representation of IS. Resolution will be dealt with in more detail in sec. 4.</Paragraph>
    <Paragraph position="2"> The principles composing the representation are worked out formally in sec. 5. Here is an intuitive overview: the arrows pointing directly to the FOC and BG partition originate from accenting or nonaccenting of the single words, respectively. The additional arrows between the constituent nodes are introduced by the grammatical principles of F-projection irrespective of the actual prosodic marking. This becomes clear when we regard the following alternative prosodic marking of (19):</Paragraph>
  </Section>
  <Section position="6" start_page="671" end_page="672" type="metho">
    <SectionTitle>
BG FOG
</SectionTitle>
    <Paragraph position="0"> Note that here, the dashed arrow from begriiflt to ihren Besuch is overruled right away, since the accented begriiflt is strictly tied to FOC. The  phrase ihren Besuch is forced into tile BG partition, thus the utterance is correctly predicted to be restricted to contexts where Besueh is given. As anticipated above in tile discussion of the lexical ambiguity involved, this conelusioil can be drawn even if other points remain underspecified.</Paragraph>
  </Section>
  <Section position="7" start_page="672" end_page="673" type="metho">
    <SectionTitle>
4 Resolution
</SectionTitle>
    <Paragraph position="0"> An underspecified IS arising from tile prosodic marking of a sentence can be resolved by information from the context. As noted above, entaihnent by context introduces additional solid line arrows.</Paragraph>
    <Paragraph position="1"> rlb covet&amp;quot; more than just trivial cases, the (:ounterpart of Schwarzschild's (1995) F-skeleton has to bc kept track of in the underst)ecified representation.</Paragraph>
    <Paragraph position="2"> At first glance, this seems to be incompatible with the idea of underspeeification, since the F-skeleton that is checked against the context for entailment, requires settlement on what the actual F-marking is. For instance, to check the givenncss of the VP in (23), reads a book about X has to be entailed, whereas on the basis of the marking in (24), reads Y has to be entailed.</Paragraph>
    <Paragraph position="3"> (23) I%anz liest ein Buch filler \[S('ml&amp;quot;FE.\]F l~'anz reads a book about ships (24) bYanz liest \[ein Buch filler \[ScHnq&amp;quot;m\]F\]F The solution lies in the observation that the latter F-skeleton entails the former. So, when a certain constituent (e.g., again the VP in the abow~ examples) is checked for givenness, it suffices to assume F-marking of the maximal potentially F-marked subconstituents (I call this the maximality assumption). If it turns out that the actual F-marking is more restricted, this will be detected at a lower level. For example, if (23) is the right solution, this will be discovered even if reads a book about X is not checked, since in this case, a book about X will be contextually given as well.</Paragraph>
    <Paragraph position="4"> To illustrate resolution in tile graph representation, take the following example in context: (25) a. Amta hat Otto fotografiert.</Paragraph>
    <Paragraph position="5"> Anna has Otto photographed l). HANS hat Otto ein Bv(,n gegeben.</Paragraph>
    <Paragraph position="6"> Hans has to-Otto a book given Sentence (25t)) produces the following graph: (Hans hat Otto ein Buch gegeben,</Paragraph>
    <Paragraph position="8"> The nodes are now labelled by pairs. The first element of a pair is tile semantic wflue of the constituent corresponding to the node (here again expressed inforlnally in natural language); the second eleinent is the F-skeleton based on the maximality assumption - the F-skeleton is obtained by (i) replacing the maximal F-marked subconstituents (or sister constituents, in the case of indirect F-marking of the head, following (12b)) by a variable, (it) existentially binding unfilled arguments, and (iii) existentially quantifying over the variables from the F-skeleton (cf. also fit. 7). The latter quantification is restricted by the set of contextually salient values C.</Paragraph>
    <Paragraph position="9"> In resolving underspecifieation from context, it is checked for each node with access to the BG t)artition ~t whether its F-skeleton is entailed by an antecedent in the context. For gegeben and the lowest verb projection ein Buch gcgeben, there is no such antecedent in the context. However, for the VP Otto cin Bueh gegeben the VP from (25a) Otto fotografiert is a suitable antecedent: after existential binding, (~x) fotografieren(x,Otto) entails (~R C C)(3x)\[R(x,Otto)\]. Similarly for the con&gt; plete sentence: fotogrMieren(Anna,Otto) entails (3e, u C C)\[P(u)\]. So, solid line arrows replace the two dashed arrows pointing to BG (suggested in (26) by tile longer dashes).</Paragraph>
    <Paragraph position="10"> The status of tile lower verb projections in (26) is still underspecified. If a wider context was considered, antecedents could possibly be found, so it makes sense to end 1, t) with such a representation after processing the discourse (25). Once we know that all salient context has been considered, a rule of I'bcus Closure is at)plied. This strengthens the arrows pointing towards FO(\] for all unresolved constituents, t)redicting eiu Buch .qcgcben as the focus for the example. In an at)plication, heuristics may trigger Focus Closure earlier, to aw)id unneecessary inferences.</Paragraph>
    <Paragraph position="11"> The representation proposed here comes close to Sehwarzschild's (1995) theory of F-marking in coverage, .2 avoiding the computationally ext)ensive disjunction of alternative analyses in favour of a single graph reI)resentation that is under-specified when based on sentence internal infern Constraining the givemmss check to nodes with access to the BG partition makes sure that narrow (eontrastive) focus on given entities (like in (17)) is treated correctly. Since all acce.nt on a word introduces just an arrow towards FOC, narrow focus on a word survives the check even in cases where the word is given.</Paragraph>
    <Paragraph position="12"> 12For examples with several ambiguous accents, the modified account collapses some F-markings with minimal diffcrm,ces in inte.rpretation into one. For instance, two of the twelve F-markings for (i) are indistinguishable: (it) and (iii). A context that wouhl enforce the latter in Schwarzschild's theory tlrodu(:es (it) in the underspecitied account.</Paragraph>
    <Paragraph position="13">  mation only. l~lrthermore, Schwarzschild's pragmatic condition Avoid F that selects the analysis with the least F-marking (cf. fn. 8) is no longer needed.</Paragraph>
  </Section>
  <Section position="8" start_page="673" end_page="673" type="metho">
    <SectionTitle>
5 HPSG principles
</SectionTitle>
    <Paragraph position="0"> The representation proposed in sec. 3 and 4 can be implemented directly in a sign-based formalism like HPSG. In this section, tile central composition principles for German are worked out. A binary branching structure is assumed. Again, the representation will be fairly open as to which particular semantic formalism is chosen. This is reflected in tile Semantics Principle I assume, which specifies the semantic value of a phrase as the application of a two-place function compose to the semantic values of both daughters. The function can be spelt out in different ways depending on the choice of a semantic theory, la Furthermore, a function variable is assumed that maps a semantic object to a new variable of the same type.</Paragraph>
    <Paragraph position="1"> The HPSG type cont (the value of the CONT(ENT) feature) has the following four new features: O-SEM ('ordinary semantics') and I,'-SKEL (F-skeleton) of the type of a semantic object, tile set-valued IS-CSTR (IS constraints) and the binary MAX-F (for potential maximal focus).</Paragraph>
    <Paragraph position="2"> The phonological information is enriched by a feature PROM (prominence) with values accented and unaccented.</Paragraph>
    <Paragraph position="3"> The following principles specify the lS-CSTR set for a sign, introducing arrows, or links, between  However, such a context is quite intricate to construct. Here is an example: (iv) Der Direktor der Firma ABC sat~ im C~f~.</Paragraph>
    <Paragraph position="4"> The director of company ABC sat in-the care Der Kellner begriiflte eine Bekannte.</Paragraph>
    <Paragraph position="5"> The waiter greeted a friend Context (iv) does not entail der Direktor der X begriiflte Y, so (ii) is ruled out according to Schwarzschild's system. The resolution process proposed in this paper is based on the maximality assumption, and thus checks givenness for the complete sentence only once, with the complete subject F-marked. To rescue the difference between (ii) and (iii), it would have to be enforced that resolution of the subject NP takes place before the resolution of the focus projected from the object. This is a conceivable solution - however, declarative perspiguity would be sacrificed for a very moderate benefit, considering the main point of this paper.</Paragraph>
    <Paragraph position="6"> lain the example below, simple predicate-argument semantics is used for illustration.</Paragraph>
    <Paragraph position="7"> semantic objects. (Tim IS partitions/oc and bg are here also treated as semantic objects.) The h_link relation corresponds to the obligatory (solid line) arrows in the graphs, s_link reflects defeasible (dashed line) arrows. In the following, the link relations are expressed verbally. (27) is the counterpart to (11); (28) and (29) reflect clauses (12a) and (12b).</Paragraph>
    <Paragraph position="8"> (27) Focus Linking Principle The O-SEM value of a pitch accented word is h_linked to foe.</Paragraph>
    <Paragraph position="9"> (28) Head F-Projection Principle The O-SEM value of a phrase is s_linked to the O-SEM value of its head daughter.</Paragraph>
    <Paragraph position="10"> (29) Indirect Head F-Marking Principle In a head-complement-structure, where none of the head daughter's arguments have yet been saturated, 14 the O-SEM of the head daughter is s_linked to the O-SEM value of the complement daughter.</Paragraph>
    <Paragraph position="11"> These three principles establish direct or indirect links towards foc. For the constituents that are not obligatorily focus marked, the underspecified representation requires additional defeasible links to bg: (30) Background Linking Principle The O-SEM value of every sign that is not accented is s_linked to bg.</Paragraph>
    <Paragraph position="12"> The principles just presented compose the representation introduced in sec. 3, with the nodes in the graph corresponding to the O-SEM values.</Paragraph>
    <Paragraph position="13"> To provide the input for the resolution routine, the representation was enriched in sec. 4 by the F-skeleton. This is kept track of in the F-SKEL feature (assuming independent existential binding of unfilled argmnents and free variables).</Paragraph>
    <Paragraph position="14"> (31) F-Skeleton Instantiation The F-SKEL value of a word with \[O-SEM (~\] is (i) the function variable(a), if ~ is h_linked to foc; (ii) a, if the word is marked \[MAX-F __\];15 (iii) eomposition(a,fl) (where fl is the F-SKEL value of the word's complement), if the word is marked \[MAX-F J-J, but a is not h_linked to foe.</Paragraph>
    <Paragraph position="15"> (32) F-Skeleton Principle The F-SKIn, value of a phrase is the function compose applied to (i) the F-SKEL vahm of a daughter with</Paragraph>
  </Section>
  <Section position="9" start_page="673" end_page="674" type="metho">
    <SectionTitle>
\[MAX-F --\]; or
</SectionTitle>
    <Paragraph position="0"> (ii) the function variable(a) of a daughter with \[MAX-F J-\] and \[O-SEM O~\]; for both daughters.</Paragraph>
    <Paragraph position="1"> 14This formulation will be subject to changes once there is a clear concept of integration (cf. fn. 6) - (29) applies to integrated constitnents.</Paragraph>
    <Paragraph position="2"> lSThe feature MAX-F is actually redundant. It has been introduced for convenience, signifying that a chain of links to foe exists - a condition that could be checked directly in the graph. But it does not hurt much to carry the feature along in the principles (27) (29).</Paragraph>
    <Paragraph position="3">  A sample analysis for (33), a slight simplifi('ation of (25b), is give.n in fig 1. The graph produced by the linking constrnints is the one in (26).</Paragraph>
    <Paragraph position="4"> (an) (Ich weifi, daft) HANS Otto ein BUCH gab.</Paragraph>
    <Paragraph position="5"> I know that Hans to-Otto a book gave Let us briefly see how the principles interact to produce the phrase ein \]3uch gab (For simplicity, the NP is treated as if it was a word). Since tin Buch bears a pitch accent, the Focus Linking Principle (27) applies, introducing an obligatory link to FOC (h_link(\[\], foe)). For the unaccented gab, the Background Linking Principle applies, giving rise to a defensible link (s_link(N, bg)). At phrase level, the Indirect Head F-Marking Principle (29) and the Head F-Marking Principle apply (introducing s_link(g\],N) for the head, and s_link(N,iN) for the phrase, respectively). In addition, (27) applies again: s_link(iN, bg).</Paragraph>
    <Paragraph position="6"> As for the F-Skeleton, subclause (i) of (31) applies at ein Buch, subclause (iii) at gab, causing the function compose to apply to gab's own semantic value and to its sister's F-SKEL value. The phrase is covered by (32), where both daughters are marked \[MAX-F +\] and thus fulfil subclause (ii).</Paragraph>
  </Section>
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