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<Paper uid="C90-2018">
  <Title>Feature Logic with Disjunctive Unification</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> 1. t. Ambiguity in Nat;ural \]\[,anguage Our use of language mirrors our intellectual capacities, which are as yet my no mea.ns understood. As long as we can not formally de.scribe the processes involved in thinking and understanding, k)rnlM descriptions of human language have to b&lt;: rough approximations. One pa.rticular instance of this general fact is; the problem of disambiguation of human utterances. Since our use of words fits our capabilities of itnderstanding l.heir meaning, contex:t and intent, systems that do ilot have such capabilities can, at best, produce sets of possible analyses. It is well known that such sets can be very la.rge in practice.</Paragraph>
    <Paragraph position="1"> Ambiguity in aatnral language is fed by a couple of source.~;, including lexicat ambiguity, where differing analyses are possible for a given word concerning its part of speech, subcat.cgorization for complements, morphological features, or any o!her information assigned to it, and structural ambiguity introduced by different possible groupings or interpretations of phrases or different interrelaIious between them with respect to subcategorizatioil, meaning, pragmMics etc. On each le.vel, a. bunch of possibilities exist, which could po-tentially multiply to an enormous space of combinations.</Paragraph>
    <Paragraph position="2"> l lowever, these possibilities interact and restrict each other in such a way, that taking it all together - only a few (hopcfulJy exactly one)interpretations remain.</Paragraph>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
1.2 Unification-Based Formalisms
</SectionTitle>
      <Paragraph position="0"> For about a decade, many fornral theories of naturM lan-.</Paragraph>
      <Paragraph position="1"> guage haw: tried to describe their subject in terms of so called feature structures, i.e. potentially nested bundels of features that are assigned to words and phrases. These structures are sometimes seen as M)stract linguistic objects, which are described using a suitable description language, sometimes they are given ~ concrete shape in form of finite automatons and regarded themselves as descriptions of the linguistic objects \[Kasper/Ronnds 86\]. Despite such differences in interpretation, there is a consensus among the theories that linguistic descriptions should provide constraints concerning feature structures and that a set. of such constraints gives a partial description of the feature st, rnctures associated with a phrase. A set of constraints defines a milli real model, i.e. a rninimM structure satisfying all constrainls in the set. The union of two sets of constraints sot (ontra..</Paragraph>
      <Paragraph position="2"> dieting each other leads to a minimal model which is the least common extension of the models of both sets. Sn(-h minimal common extensions can be constructed by unification of the given models, hence the term unification-based form alisrns.</Paragraph>
      <Paragraph position="3"> There is also a consensus among feature-based ti~eories that ambiguity should be described with disjunctive formulas, and most formalisms offer ways to spe(:it} them. If disiunc tlon is present, there is usila.l}y a. tinite ltumber el minimal models instead of only one. Ilowever, until now, the way such disjunctive specifications have been processed compu taiionally was not quite satisfactory. An enumeration of the possibilities using a backtracking scheme or a chart, which c.orresponds to an expansion to disjunctive nornlal form in the underlying logic, often leads to computational ineflMency.</Paragraph>
      <Paragraph position="4"> Approaches to improve the situa.iion both ill terms of the logic and the inlplementation (see e.g. \[l(arttuncn 81, Ka.'q~er 87, Eisele/Dgrre 88, Maxwell/Kaplan $9\]) can be subdivided in those assuming di:,junctive value.s tor fealures and lhose allowing \[or more general terms of disjunction.</Paragraph>
      <Paragraph position="5"> Roughly, we can state that fornia.lisms and implementatio;is that provide wilue disjunction can be implelnented more eas ily a.nd more efiicienilg', since they can exploit the faci that disjunclive information for a certain feature ha~; no et\[ect (~li other features (as long ;is disjunctive iui\3rnlation .'loe~ not interact with path equivalences, see \[Eisele/1)grre g8\]). t3tlt. the restriction to wdue disjunction decreases the expressive power of the formalism, since disjunctions concerning di\[ l\?rent features must be stated on a higher level, Schemes providing for general disjunction allow for a more compact representation of such cases. But if disjunctive information is not local to single features, the interaction between different parts of tile descripi.ion is more dilflcuh to handle (see e.g. \[Kasper 87\]).</Paragraph>
      <Paragraph position="6"> The method we propose combines advantages of both ap preaches. It can be seen as a generalization of value disjunction, which allows for a concise description of di~Lju~c-Lion concerning more than one feature, or pat;h. It can also be se.en as an efficient implementation of general disjunctiol~ which a.llows to exploit the locality of disjunctive information whenever this is possible.</Paragraph>
    </Section>
  </Section>
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