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<Paper uid="C00-2161">
  <Title>Querying Temporal Databases Using Controlled Natural Language*</Title>
  <Section position="4" start_page="1076" end_page="1076" type="metho">
    <SectionTitle>
3 The TDB
</SectionTitle>
    <Paragraph position="0"> A TDB is a two-sorted tirst-oMer structure.</Paragraph>
    <Paragraph position="1"> The domain consists of a Data Do'main, D, and a Temporal Domain of intervals, 7'/, detined as follows. Let Tp 1)e a. set (of time points) with a discrete linear order without endl)oints, &lt;._ .7'1 is defined as the set of pairs : 7) = Z,)la _&lt; b c Tu{-oo, oo}}. a rdational database schema is a set, of single-sorted predicate symbols (H,1,..., l~k). Given a relational database schelna p, a Tl)l} schema p' is the sol; 3/ of two-sorted predicate sylnbols (lPS11,..., \]~), where the sort of /C/~ is D aritv(l~i) x TI. A TI)13 instance of schema f is a set of relations R\[ C l) arity(l{i) X 7), where each R~ is finite.</Paragraph>
    <Paragraph position="2"> For instance, assume a database schema p consisting era single binary predicate symbol 'work, storing lbr each elnployee the department ill which she is employed. The Tl)l} schema p' consists of the relation wo'rk', called a validti'mc state table, which adds a. temporal argunlent 1;o the original relation, caJled the validtime of the table. '\['he temporal argument can be used to store the history (and 1)erhaps even future plans) of departments in which eml)loyees are employed. Following a. suggestion of (Androutsopoulos, 1996), we also include relations mal)l)ing names of ca.lendricat items to temporal intervals in p'. For instance, we store a. relation year / ma.l)l)ing the year 2000 to the interval \[71. \].2(100-3 J. 12.2000\] (which in turn is n lappe(t to an element of 7)).</Paragraph>
    <Paragraph position="3"> We now describe the translation process.</Paragraph>
  </Section>
  <Section position="5" start_page="1076" end_page="1078" type="metho">
    <SectionTitle>
4 The translation process
</SectionTitle>
    <Paragraph position="0"> The translation 1)recess a.ccepts input NL questions in a controlled subset of Nil,. Restricting inl)ut language in this way enables e\[l'ective processing of a sufficiently rich fragment while avoiding many of the well-know problems of unrestricted NI,. We use a formal grammar in the TLG framework. Our grammar is specially designed for use with ~ particular TDB schema.</Paragraph>
    <Paragraph position="1"> Future work will allow easier configuration of the grammar with respect to the schema.</Paragraph>
    <Paragraph position="2"> Our grammar is based on work on all independently motivated theory of the semantics of telnt)orality. Most of the research in this tield (see (Steedman, 1997) for a survey) has rocllsed on the issues of tense a.nd aspect. \~e ha.ndle tense, but purposefully not aspect, which plays  an import,~nt role in (Androutsol)oulos , 1996).</Paragraph>
    <Paragraph position="3"> Aspect, which is used to retlect speal~ers' temporal viewpoint with respect to reported situations is an imi)ortant facet of NL temporality. However, its relevance to TDBs is questionable, as it is unlikely that a realistic TDI3 would actually encode such subjective viewpoints. Moreover, handling aspect requires postulating a more complex data model. For instance, (Androutsopoulos, 1996) augments tile TDB model with event-like &amp;quot;occurrence klentifiers&amp;quot;, and adds a.n additional argument to temt)oral relations indicating whether a given event has cuhninated or not. While such devices may perhaps be linguistically justified, it is unclear whether the TDI3 community would adopt such augmentations of the model.</Paragraph>
    <Paragraph position="4"> Instead, following (Pratt and Vrancez, 2000; Nelken and Francez, 1999) our focus is on sentences modified by temporal PPs. These PPs are analyzed as variants of standard generalized quantifiers (Barwise and Cooper, 1981), in which qnantification is over: time. Using this framework, we handle questions that refer explicitly to the temporal (timension (e.g.</Paragraph>
    <Paragraph position="5"> When/during which year ...) as well as questions in which temporality is hnplied by the TI)B context (e.g. Did Mary work in marketing?, Which employees worked in marketing?). We ban(lie both clausal a.nd phrasal teml)ora\] Pl)s (e.g. after John worked in R&amp;D, during every year). J\n important strength of this semantic theory is that it; allows for arbitrary iteration of PPs (e.g. one month during every year until 1992). In addition, our grammar also handles qua.ntific~tion over individuals (e.g. some employee), coordination and negation.</Paragraph>
    <Paragraph position="6"> input questions are parsed using a lexicalized type-logical grammar. Lexical items are ass(&gt; elated with a syntactic category and a higher-order lambda-term representing its semantics. Taking advantage of 'I'LG's elegantly tight coupling of syntax and semantics, parsing and construction of a semantic representation in the form of an LAlle n Ibrmula proceed silnultaneonsly, in a bottom-up fashion. \Y=e have found using TLG to be advantageous over a feature-structure based formalism (such as IIPSG as in (A ndroutsopoulos, 1996)), since formula construction is an integral part of the l)arslng and does not require complex ad-hoc manipulations of feature structures.</Paragraph>
    <Paragraph position="7"> Using a particular grammar helps reduce some of the ambiguity inherent in unrestricted NL. For instance, whereas in general a preposition such as at is ambiguous between a temporal and a locative interpretation, the choice of the coml)lement NP relative to a given schemainduced grammar deterministically fixes the interpretation. As another example, whereas iterating several temporal PPs (e.g. during some month every year) opens up exponential seeping possibilities, some choices are eliminated by world knowledge, which is encoded in the grammar (e.g. every year must have higher scope than some month since months are included in years and not vice-versa). In cases of remaining ambiguity, Cite user is presented with all Cite distinct possibilities. Future work will allow the user: to lnalce informed choices between different possible readings, e.g. by presenting him with NL l)ara.phrases of the alternatives.</Paragraph>
    <Paragraph position="8"> \Y=e translate NI, questions into \],All(',,,- if'ire main reason for: not translating directly to SQl,/Temporal is that the \]atter is not closed \['or sub-formulae, i.e. a sub-formula of a well-formed query is not necessarily well-formed.</Paragraph>
    <Paragraph position="9"> Since LAne, &amp;quot;is closed for&amp;quot; sub-formulae, compositionally constructing formulae while parsing in a bottom-u 1) fashion becomes much easier.</Paragraph>
    <Paragraph position="10"> I, An~, is defined as follows (Toman, 1996).</Paragraph>
    <Paragraph position="11"> I,et p be the database schema (1~,..., I~t,.). l,et:</Paragraph>
    <Paragraph position="13"> where x,y are variables over D, x is a vector of such variables, l, J are varlet)los or constants over T\], and (r is one of the operators: precedes, meets, overlaps, equals, contains. LAlien is defined as tile set of' \[brmulae p E L that con-Lain at most one free variable over TI. The answer to a formula 90 relative to a TDB D is {x, ll&gt; ~ :(x, :)}.</Paragraph>
    <Paragraph position="14"> To illustrate, consider the NL question: During which years did Mary work in marketing? 'File I,Alle n representation for&amp;quot; it is constructed in a bottom-up nla, nnel'. The meaning representation of the main clause Mary worked in marketing is constructed as:</Paragraph>
    <Paragraph position="16"> In this formula, I denotes a Reichenbachianlike reference time, J denotes a time interval  (I,ring which Mary worked in nia,rl(eA:\]nlg, which is loca,l;od in the l)a,sl; (l;he conl;ribution ol7 the t, onse) a, nd is hicluded wil;hin 1.</Paragraph>
    <Paragraph position="17"> The me~miug o\[&amp;quot; the \['ull (lll(~,~lJon \]8 COilstructed 1)y a,l)t)lying th(; Inca, sing o\[' the \]lll;orrclga,1;ive ton~l)oi:a,1 1)1 ) during which year i;o the lllea,ning o\[' Lho c.\[a, uso. \Y=il;\]io.t going \]lifO (lcta, ils, l;ho r('~s, lt is: A./ Cpa,,~tAJ C\]) The effect of applying the 1)1 ~ is that 1;lie wu'iable / is now 1)ol;h free ~ul(l rest;rioted to 1)e {\]lo time of a, yea, r. The a,liswer 1;o l:li(; I'orin.la, is ~lie so{ o\[&amp;quot; ilitoi:vaJ,~ \] 1;ha,t a, re. ye4~,i',% a,n(I (lur-\]ilg whi(:h 1;\]ioro is a,n iill;orva,l ,\] COliLaiil0d ill tlle~ l)asl;~ (l.ring whi(:h ~l/\]il.rry work(,(l ill llla,rl,:ol,ing. VVo allow \]l;ol:a,1;od I)l)s 1;o a,l)l)iy ili a, siniila,r  once Lo hiterva,\]s. We \]ia,v(; \['ound using a, syl'il;actica,lly i:osl, ri(:l;ed vel:8iOli of' I,All&lt;;n 1;o t)e a,(iv,anl;ageous, a.s il; a cl;ua,lly sire plifie;~ the tra n,~lation. null (\]oni;in,ing oil r i)reviou,~ oxa,lllt)le&gt; 1;lie rostlltillg I~Alle. rOl:lllllla, iS StllJS0.(tllonl;iy IA'P.,llSla,l,(,(l into tile \['ollowing S(~\]JTcnli)oral (lu(;ry:  The (ltl(;ry :a,sks for the first a,rglunon{ of tlio rela, tion \]nsi41,1lCO yeal J such tiia, t the refection \]IIM,a,IlCO work # in(:lu(los a, 1;ul)lo consisting of 'Mary'~ 'marketing' a, nd a, va,lid time. which is l;oml)orally iucl.dc'(l in the wind l;ime of&amp;quot; the yea, r, as well as in the \]nl;ol:va,l sl;:4,1:l;ing a,1; the ~\])Ogillllilig ~ O\[' (;\]1110 i/,ll(\] (ql(l\]n~ :llOW :- V\]Z. l, he~ past. The 'l'l)l~ rt;,~polMs 1)y returning a table conl,aini,&lt;e; exactly 1;ho re(ltleslx;d year names.</Paragraph>
  </Section>
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