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<Paper uid="P95-1048">
  <Title>Semantic Information Preprocessing for Natural Language Interfaces to Databases</Title>
  <Section position="3" start_page="0" end_page="314" type="metho">
    <SectionTitle>
2 LDT, AET and RLDT
</SectionTitle>
    <Paragraph position="0"> LDT and AET. LDT was introduced for a system, where input is a logical formula, whose predicates approximately correspond to the content words of the input utterance in natural language (lexical predicates). Output is a logical formula, consisting of predicates meaningful to the database engine (database predicates). AET provides a formalism for describing how a formula consisting of lexical predicates can be tranlsated into formula consisting of database predicates. The information used in the translation process is an LDT. A theory r contains  horn clauses v(p~ A... A P,, --* Q) or universal conditional equivalences v(P1 ^... ^ P. ~ (RI ^... ^ Rz -= F)) or existential equivalences</Paragraph>
    <Paragraph position="2"> where Pi, Ri denote atomic formulas, Q denotes a literal, F denotes a formula and V denotes universal closure. The LDT also contains functional relationships that are used for simplifications of the translated formulas and assumption declarations. Given a formula Fting consisting of lexical predicates and an LDT, AET tries to find a set of permissible assumptions A and a formula Fab consisting of the database predicates such that F u A =~ V(Fti,g = Fab) The translation of Fzi,g is done one predicate at a time. For each predicate in the formula Fting, there is a so-called conjunctive context that consists of conjuncts occurring together with the predicate in Fting, meaning postulates in the theory P, and the information stored in the database. Given an LDT, this conjunctive context determines how the predicate will be translated by AET.</Paragraph>
    <Paragraph position="3"> As an example, suppose that the lexical representation of the sentence Is there a student who takes</Paragraph>
    <Paragraph position="5"> Suppose that the theory r consists of axioms:</Paragraph>
    <Paragraph position="7"> where student, take and unknown are lexical predicates and db_student, rib_course, db_take are database predicates 1. Also suppose, that the LDT declares as an assumption aeourse(X), which can be read as &amp;quot;X denotes a course&amp;quot;.</Paragraph>
    <Paragraph position="8"> Part of the conjunctive context associated with formula take(E, X, Y) in Ftlag is a formula (5).</Paragraph>
    <Paragraph position="10"> According to the translation rules of AET, axiom (2), and a logical consequence of a conjunctive context (6), the formula take( E, X, Y) can be translated</Paragraph>
    <Paragraph position="12"> Formulas student(X), take(E, X, Y1), unknown(Y, cmpt710) and unknown(Yl, cmpt720) are translated similarly. Assuming crept710 and crept720 are courses, the input Fsi,g can be rewritten into Fdb shown below.</Paragraph>
    <Paragraph position="14"> So we can claim that Fab and Fzin9 are equivalent in the theory F under an assumption that crept710 and crept720 are courses.</Paragraph>
    <Paragraph position="15"> RLDT. We shall constrain the expressive power of the LDT to suit tractability and efficiency requirements. null We assume that the input is a logical formula, whose predicates are input predicates. We assume that input predicates are not only lexical predicates, but also unresolved predicates used for, e.g., compound nominals (Alshawi, 1992), or for unknown words, as was demonstrated in the example above, or synonymous predicates that allow us to represent two or more different words with only one symbol.</Paragraph>
    <Paragraph position="16"> The output will be a logical formula consisting of output predicates. We do not suppose that the output formula contains pure database predicates.</Paragraph>
    <Paragraph position="17"> However, we allow further translation of the output formula into database formulae using only existential conditional equivalences. The process can be implemented very efficiently, and does not affect selectional restrictions of the input language.</Paragraph>
    <Paragraph position="18"> We assume that each atomic formula with input predicates can be translated into an atomic formula with output predicates. An RLDT therefore also aThe predicate unknown will be discussed in the next section.</Paragraph>
    <Paragraph position="19"> contains a dictionary of atomic formulas that specifies which input atomic formulas can be translated into which output atomic formulas.</Paragraph>
    <Paragraph position="20"> Existential equivalences in KLDT's logic will not be allowed. We also assume that F in the universal conditional equivalences is a conjunction of atomic formulas rather than arbitrary formula.</Paragraph>
    <Paragraph position="21"> We demand that an RLDT be nonrecursive. Informally RLDT nonrecursivness means that for any set of facts A, if there is a Prolog-like derivation of an atomic formula F in the theory F U A, then there is a Prolog-like derivation of F without recursive calls.</Paragraph>
  </Section>
  <Section position="4" start_page="314" end_page="315" type="metho">
    <SectionTitle>
3 The Normalization Process
</SectionTitle>
    <Paragraph position="0"> Our basic idea is to preproeess the semantic information of KLDT to create patterns of possible conjunctive contexts for each lexical predicate. The result of the preprocessing is a normalized KLDT: the collection of the lexical predicates, their meanings in terms of the database, and the patterns of the conjunctive contexts.</Paragraph>
    <Paragraph position="1"> First we introduce the term (Nontrivial) Normal Conditional Equivalence with respect to an RLDT T ((N)NCE(T)).</Paragraph>
    <Paragraph position="2"> Definition: Let T be an RLDT and F be a logical part of T. The quadruple (A, C, Fim,,t, Fo,,put) is NCE(T) iff C is a conjunction of input atomic formulas of T, A is a conjunction of assumptions of T, and formulas</Paragraph>
    <Paragraph position="4"> are logical consequences of the theory F (we shall refer to the last condition as soundness of the NCE(T)). We shall call the quadruple (A, C, Fi,put, Foutv,,t) nontrivial NCE(T) (NNCE(T)) iff formula C A A does not imply truth of Foutp,,t in the theory F.</Paragraph>
    <Paragraph position="5"> Informally it means that Fi,p,,t can be rewritten to Fo,,tp,t if its conjunctive context implies A and does not imply the negation of C. (A, C) thus can be viewed as a pattern of conjunctive contexts, that justifies translation of Finput to Foutput.</Paragraph>
    <Paragraph position="6"> We allow RLDTs to form theory hierarchies, where parent theories can use results of their children's normalization process as their own logical part.</Paragraph>
    <Paragraph position="7"> Given an I~LDT T, for each pair consisting of the ground lexical atomic formula Fi,put and the ground database atomic formula Fo,,tput from the dictionary of T, we find the set S of conditions (A, C) such that (A, C, Fi,,pu,, Fo,,p,,) is NCE(T). We shall call the set of all such NCE(T)s a normalized R.LDT.</Paragraph>
    <Paragraph position="8"> If Fi,put and Fo,,tp,t contain constants that do not occur in the logic of RLDT, the generalization rule of FOL can be used to derive more general results by replacing the constants by unique variables.</Paragraph>
    <Paragraph position="9">  If the T does not contain negative horn clauses of the form P ---* notQ then the following completeness property can be proven: If (A1, C1, Fi,e,~, Fox,put) is NNCE(T) and S is a resulting set for the pair Finput, Foutp~t then there are conditions (A, C) in S, such that AAC is weaker or equivalent to Ax A C1.</Paragraph>
    <Paragraph position="10"> The normalization process itself is based on SLDresolution(Lloyd, 1987) which we have chosen because it is fast, sound and complete but still provides enough reasoning power.</Paragraph>
    <Paragraph position="11"> Using the example from the previous section, the normalization algorithm when given the pairs (student(a), db_student( a ) ), ( unknown( a, b ), db_course(a, b)) and (take(e, a, b), db_take(e, a, b)) will produce the results {(true, true)}, {(aeour,e(b), true)} and {(acourse(X), student(a) A unknown(b, X)} respectively.</Paragraph>
  </Section>
  <Section position="5" start_page="315" end_page="315" type="metho">
    <SectionTitle>
4 The Construction of Selectional
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="315" end_page="315" type="sub_section">
      <SectionTitle>
Restrictions
</SectionTitle>
      <Paragraph position="0"> The normalized RLDT is used to construct selectional restrictions.</Paragraph>
      <Paragraph position="1"> We assign the tags &amp;quot;thing&amp;quot; or &amp;quot;attribute&amp;quot; to argument positions of the lexical predicates according to what kind of restriction the predicate imposes on the referent at its argument position. If the predicate is a noun or the referent refers to an event, we assign the tag &amp;quot;thing&amp;quot;. If the predicate explicitly specifies that the referent has some attribute - e.g. predicate big(X) specifies the size of the thing referenced by X and predicate take(_, X,_) specifies that the person referenced by X takes something - then we tag the argument position with &amp;quot;attribute&amp;quot;.</Paragraph>
      <Paragraph position="2"> The normalized RLDT allows us to compute which &amp;quot;things&amp;quot; can be combined with which &amp;quot;attributes&amp;quot;. That is, we can determine which words can be modified or complemented by which other words.</Paragraph>
      <Paragraph position="3"> We assume that the normalized RLDT has certain properties. Every NCE(T) that describes a translation of an &amp;quot;attribute&amp;quot; must also define a &amp;quot;thing&amp;quot; that constrains the same referent, e.g. the NCE(T) (true, person(X) A drives(E,X,Y), big(Y), db_big_car(Y)) for translation of the predicate big(Y) does not fulfil the requirement but NCE(T) (true, car(Y), big(Y), db_big_car(Y) ) does.</Paragraph>
      <Paragraph position="4"> We also assume that if a certain &amp;quot;thing&amp;quot; does not occur in any of the NCE(T)s that translates an &amp;quot;attribute&amp;quot; then the &amp;quot;thing&amp;quot; cannot be combined with the &amp;quot;attribute&amp;quot;.</Paragraph>
      <Paragraph position="5"> Using the example above and the assignments</Paragraph>
      <Paragraph position="7"> take(E, X, Y) E is a &amp;quot;thing&amp;quot;, X and Y are &amp;quot;attributes&amp;quot; we can infer that student(X) can be combined with attribute take(_, X,_) but cannot have an attribute take(_,_,X).</Paragraph>
      <Paragraph position="8"> To simplify results, we divide &amp;quot;attributes&amp;quot; into equivalence classes where two &amp;quot;attributes&amp;quot; are equivalent if both attributes are associated with the same set of &amp;quot;things&amp;quot; that the attributes can be combined with. We then assign a set of representatives from these classes to &amp;quot;things&amp;quot;.</Paragraph>
      <Paragraph position="9"> To be able to produce more precise results, we distinguish between two &amp;quot;attributes&amp;quot; that describe the same argument position of the same predicate according to the &amp;quot;thing&amp;quot; in the other &amp;quot;attribute&amp;quot; position of the predicate, when needed. Consider for example the preposition &amp;quot;on&amp;quot; as used in the phrases &amp;quot;on the table&amp;quot; or &amp;quot;on Monday&amp;quot;. We handle the first argument position of a predicate on(X,Y) associated with the condition table(Y) as a different &amp;quot;attribute&amp;quot; as compared to the condition monday(Y).</Paragraph>
    </Section>
  </Section>
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