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<Paper uid="E95-1002">
  <Title>Principle Based Semantics for HPSG</Title>
  <Section position="2" start_page="0" end_page="10" type="intro">
    <SectionTitle>
1 Introduction
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    <Paragraph position="0"> The semantic analysis of standard HPSG deviates from the familiar Montegovian way to construct semantic representations mainly in that it uses unification to eliminate the need for 13-reduction. Variables 1In the present paper we do only focus on simple principles restricting scope ambiguities and ambiguities resulting from plural NPs in English. For German restrictions on scope are much more complicated because they cannot be stated independently of scrambling phenomena. In (l~-ank/Reyle 1994) the present approach is worked out for a fragment of German that deals with (i) quantifier scope ambiguities triggered by scrambling and/or movement and (ii) ambiguities that arise from the collective/distributive distinction of plural NPs. The underlying scope theory for German was developed in (Frey 1993). The analysis in (Frank/Reyle 1994) departs significantly from our earlier account in (Frank/Reyle 1992), where monotonicity was not ensured.</Paragraph>
    <Paragraph position="1">  are bound to argument positions by the close interplay between syntactic and semantic processing; and the semantics of constituents is determined by the Semantics Principle, which governs the way of unifying the semantics of daughter constituents to build up the semantic value of the phrasal constituent: The CONTENT value is projected from the semantic head, which is defined as the syntactic HEAD-DTR in head-comp-structures, but as the ADJ-DTR in head-adjunct structures. It is important to note that the semantic contribution of quantified verb arguments is not completely projected as part of the CONTENT value. The meaning of such NPs splits into the features QUANTS, a list representing the information about quantifier scope, and NUCLEUS, containing the nonquantificational core. In the general case only the NUCLEUS is projected from the semantic head according to the Semantics Principle, while the QUANTS value gets instantiated stepwisc in interaction with the quantifier storage mechanism (Cooper Store). The mechanism of Cooper storage is built into HPSG by use of two further attributes, QSTORE and RETRIEVED, both represented as sets of quantifiers. All quantifiers start out in QSTORE by lexical definition. The Semantics Principle defines the inheritance of QSTORE to the phrasal constituents, where they may be taken out of store by an appropriately instantiated RETRIEVED value and then put into the QUANTS value of the CONTENT feature. The order in which the semantic value of quantified NPs is retrieved fixes their relative scope.</Paragraph>
    <Paragraph position="2"> To analyse sentences with scope ambiguities several parses are thus necessary. Besides the definition of appropriate restrictions to and configurations for applications of RETRIEVED the main problem we face with this kind of analysis is to modify the semantics of HPSG in such a way that it yields underspecificd representations and not sets of fully specified ones.</Paragraph>
    <Paragraph position="3"> Further shortcomings of HPSG semantics are the following. First, adjuncts (like quantificationai adverbs, modals) and also negation bear the potential to introduce scope ambiguities. In order to treat them by the same mechanism that treats the arguments of the verb their meaning representation would have to be put into store. This, however, requires further modifications of the Semantics Principle, because the treatment of head-adjunct structures differs essentially from the treatment of other configurations (see (Pollard/Sag 1994), Ch.8). 2 Second, there is no underspecified representation of ambiguities that arise from the distributive/collective distinction of plural NPs (neither within the'HPSG framework nor in the C(ore)L(anguage)E(ngine)3). Third, the semantic representation of indefinite NPs must be independent of the context in which they are interpreted. We do not want to switch from a universally quantified interpretation to an existentially quantified one, when we come to disambiguate the ambiguous sentence Every student who admires a philosopher reads his original writings such that a philosopher is interpreted specifically. This requirement calls for DRT as underlying semantic formalism.</Paragraph>
    <Paragraph position="4"> In the sequel of this paper we show how the extension of DRT to UDRT developed in (Reyle 1993) can be combined with an HPSG-style grammar. The basic idea of the combination being that syntax as well as semantics provide structures of equal right; that the principles internal to the syntactic and semantic level are motivated only by the syntactic and semantic theory, respectively; and that mutually constraining relations between syntax and semantics are governed by a separate set of principles that relate syntactic and semantic information appropriately. We will replace the Semantics Principle of standard HPSG versions by a principle which directly reflects the monotonicity underlying the interpretation process designed in (Reyle 1993): At any stage of the derivation more details are added to the description of the semantic relations between the various components of the sentence, i.e. the partial representation of any mother node is the union of the partial representations of its daughter nodes plus further constraints derived from the syntactic, semantic and also pragmatic context.</Paragraph>
    <Paragraph position="5"> 2 Quantifier Scope and Partial Orders The need for underspecified representations is by now widely accepted within computational and theoretical linguistics. 4 To make the results of the ongoing research on underspecified representations available for HPSG we may pursue two strategies.</Paragraph>
    <Paragraph position="6"> According to the first strategy we take the HPSG-style analysis - essentially as it is - and only ap2For general criticism of the analysis of adjuncts in standard HPSG see (Abb/Maienborn 1994). Their analysis of adjuncts in HPSG fits neatly into the account of semantics projection to be presented below.</Paragraph>
    <Paragraph position="7"> 3See (Alshawi 1992). In CLE the:resolution of QLFs also involves disambiguation with respect to this kind of ambiguities.</Paragraph>
    <Paragraph position="8"> 4See (Peters/vanDeemter 1995) for recent discussion.</Paragraph>
    <Paragraph position="9"> ply slight modifications to produce underspecified output. The second strategy involves a more radical change as it takes an existing theory of underspecifled representations and replaces the HPSG semantics by the construction principles of this theory. Let us start out with a sketch of the first approach.</Paragraph>
    <Paragraph position="10"> It will show us where its limitations are and allow us to compare different approaches to underspecification. The first thing to do, when un-specifying HPSG semantics, is to relax the retrieval operation. This must be done in two respects. First, we must allow NP-meanings not to be retrieved at all.</Paragraph>
    <Paragraph position="11"> This results in their relative scope not being determined. Second, we must accommodate syntactic and semantic restrictions on possible scope relations to be stated by the grammar. 5 Restrictions specifying, for example, that the subject NP must always have wide scope over the other arguments of the verb; or, that the scope of genuinely quantified NPs is clause bounded. The modifications we propose are the following. First, we incorporate the QSTORE feature into the CONTENT feature structure. This makes the NP meanings available even if they are not retrieved from QSTORE. Second, we take the value of the QUANTS feature not to be a &amp;quot;stack&amp;quot; (i.e. by appending new retrieved quantifiers as first elements to QUANTS), but allow any NP meaning that is retrieved at a later stage to be inserted at any place in that list. This means that the order of NP meanings in QUANTS fixes the relative scope of these meanings only; it does not imply that they have narrow scope with respect to the NP meaning that will be retrieved next. But this is not yet enough to implement clause boundedness. The easiest way to formulate this restriction is to prohibit projection of quantified NP meanings across bounding nodes.</Paragraph>
    <Paragraph position="12"> Thus the QSTORE and QUANTS values of a bounding node inherit the quantificational information only of indefinite NPs and not of generalized quantifiers. To be more precise, let us consider the tree /3 consisting only of the bounding nodes in the syntactic analysis of a sentence 3&amp;quot;. Then the semantic content of ~ can be associated with nodes of ~ in the following way. For each node i of fl the attributes QUANTS, QSTORE and NUCLEUS have values quantsi, qstorei and nucleusi. The relative scope between scope bearing phrases of ~, i.e. between the elements of Ui(quantsiUqstorei) can then be defined as follows.</Paragraph>
    <Paragraph position="13">  * If Q1 and Q2 are in quantsi and Q1 precedes Q2, then Q1 has scope over Q2.</Paragraph>
    <Paragraph position="14"> * If Qa is in quantsi and Q2 in quantsj, where i dominates j, then Q1 has scope over Q2.</Paragraph>
    <Paragraph position="15"> * If Q1 is in qstorei and not in qstorej, whe null re i dominates j, then Qa has scope over any Q2 in qstorejUquantsj that are not in qstoreiUquantsi.</Paragraph>
    <Paragraph position="16">  Tim last clause says that any NP Q1 occurring in the clause of level i and that is still in QSTORE has scope over all quantified NPs Q2 occurring in embedded clauses (i.e. clauses of level j). But Q1 does not necessarily have scope over any indefinite NP introduced at level j.</Paragraph>
    <Paragraph position="17"> Those familiar with the work of Alshawi and Crouch (Alshawi/Crouch 1992) might have noticed the similarity of their interpretation mechanism and what we have achieved by our modifications to standard HPSG semantics. The elements of QUANTS play exactly the same role as the instantiated metavariables of Alshawi and Crouch. This means that we could adapt their interpretation mechahism to our partially scoped CONTENT structures. But note that we already have achieved more than they have as we are able to express the clause-boundeness restriction for generalized quantifiers.</Paragraph>
    <Paragraph position="18"> We will not go into the details and show how the truth conditions of Alshawi and Crouch have to be modified in order to apply to partially scoped CONTENT structures. We will instead go ahead and work out the limitations of what we called the first strategy. To keep things as easy as possible we restrict ourselves to the case of simple sentences (i.e. to. trivial tree structures of QSTORE and QUANTS values that consist of one single node only). In this case the QUANTS value (as well as the instantiation of metavariables) imposes a partial order on the relative scope of quantifiers. Assume we had a sentence with three quantifiers, Q1, Q2 and Q3. Then the possible lenghts of QUANTS values varies from 0 to 3. Lengths 0 and 1 leave the relative scope of Q1, Q2 and Q3 completely underspecified. Values of length 2 say that their first element always has wide scope over the second, leaving all possible choices for the third quantifier. And finally we have the fully specified scoping relations given by values of length 3. There are, however, some possibilities to restrict scope relationships that cannot be represented this way: One cannot, for example, represent the ambiguity that remains if we (or, syntax and semantics) require that Q1 and Q2 must have scope over Q3, but leaves unspecified the relative scope between Q1 and Q2; nor are we able to express a restriction that says Q1 must have scope over both, Q2 and Q3, while leaving the relative scope between Q2 and Q3 unspecified. Retrieving a quantifier Qi (or starting to calculate the truth value of a sentence by first considering this quantifier) is an operation that takes Qi and adds it to QUANTS. As QUANTS is a list this amounts to a full specification of the relative scope of Qi with respect to all other elements already contained in QUANTS. This shows that the expressive power of the representation language is too restrictive already for simple sentences. We need to represent partial orders of quantifier scope. But we cannot do this by talking about a pair consisting of a quantifier Qi and a list of quantifiers QUANTS. We must be able to talk about pairs o\] quantifiers. This not only increases the expressive power of the representation language, it also allows for the formulation of restrictions on quantifier scope in a declarative and natural way. The formalism of UDRSs we introduce in the following section is particularly suited to 'talk' about semantic information contributed by diffcrent components of a sentence. It therefore provides a particularly good ground to implement a principle based construction of semantic representations.</Paragraph>
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