<?xml version="1.0" standalone="yes"?>
<Paper uid="P86-1036">
  <Title>A Terminological Simplification Transformation for Natural Language Question-Answering Systems</Title>
  <Section position="4" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(CONJ PATIENT
(VALUERESTR ICT MOTHER
DIABETIC))
</SectionTitle>
    <Paragraph position="0"> If we wanted to axiomatize the relation implied by the SEX attribute of the PATIENTS table in our database, we could readily do so by defining the role PATIENT-SEX in terms of the domain model relation SEX:</Paragraph>
    <Paragraph position="2"> These two defined terms can actually be entered into the model, and be treated just like any others there.</Paragraph>
    <Paragraph position="3"> For example, they can now appear as predicate letters in meaning representations. Moreover, to the associated data structure we can attach a translation rule, just as we have been doing with the original domain model elements. Thus, will attach to the concept PATIENT-WITH-DIABETIC-MOTHER the rule:</Paragraph>
  </Section>
  <Section position="5" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(PROJECT (SELECT FROM PATIENTS WHERE (EQ DIAMOTHER &amp;quot;YES&amp;quot;))
OVER PATID)
</SectionTitle>
    <Paragraph position="0"> The next section will illustrate how we map from expressions using &amp;quot;original&amp;quot; domain model elements to the ones we create for axiomatizing the database, using the NIKL system and its classifier.</Paragraph>
  </Section>
  <Section position="6" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
4. Recursive Terminological
</SectionTitle>
    <Paragraph position="0"> Simplification We now present the actual simplification method. It is composed of two separate transformations which are applied one after the other. The first, the &amp;quot;contraction phase&amp;quot;, seeks to contract complicated subexpressions (particularly nested quantifications) to simpler one-place predications, and to further restrict the &amp;quot;sorts&amp;quot; of remaining bound variables on the basis of the one-place predicates so found. The second part of the transformation, the &amp;quot;role-tightening&amp;quot; phase, replaces general relations in the expression with more specific relations which are lower in the NIKL hierarchy. These more specific relations are obtained from the more general by considering the sorts of the variables upon which a given relational predication is made.</Paragraph>
    <Paragraph position="1"> The contraction phase The contraction phase is an algorithm with three steps, which occur sequentially upon application to any expression of the meaning representation. First, the contraction phase applies itself recursively to each non-constant subexpression of the expression.</Paragraph>
    <Paragraph position="2"> Second, depending upon the syntactic category of the expression, one of the &amp;quot;pre- simplification&amp;quot; transformations is applied to place it in a normalized form. Third and finally, one of the actual simplification transformations is used to convert the expression to one of a simpler syntactic category.</Paragraph>
    <Paragraph position="3"> Before working through the example, I will lay out the transformations in detail. In what follows, X and X1,X2 -- Xn are variables in the meaning representation language. The symbol &amp;quot;&lt;rest&gt;&amp;quot; denotes a (possibly empty) sequence of formulae. The expression &amp;quot;(FORMULA X)&amp;quot; denotes a formula of the meaning representation language in which the variable X (and perhaps others) appears freely. The symbol &amp;quot;&lt;quant&gt;&amp;quot; is to be understood as being replaced by either the operator SETOF or the quantifier EXISTS.</Paragraph>
    <Paragraph position="4"> First, the normalization transformations, which simply re-arrange the constituents of the expressions to a more convienent form without changing its syntactic category:</Paragraph>
    <Paragraph position="6"> (2) (&lt;quant&gt; X:S (and (P X) &lt;rest&gt;) =&gt; (&lt;quant&gt; X:S' (and &lt;rest&gt;)) where S' := (CONJ S P) (3) (&lt;quant&gt; X:S (P X)) =&gt;</Paragraph>
    <Paragraph position="8"> In (2) and (4) above, the conjunction or implication, respectively, are collapsed out if the sequence &lt;rest&gt; is empty.</Paragraph>
    <Paragraph position="9"> Now the actual simplification transformations, which seek to reduce a complex sub-expression to a one-place predication.</Paragraph>
    <Paragraph position="11"> and R must be a functional role</Paragraph>
    <Paragraph position="13"> and R is functional, C an individual concept Now, let us suppose that the exercise at the end of the last section has been carried out, and that the concept PATIENT-WITH-DIABETIC-MOTHER has been created and given the appropriate translation rule. To return to the query &amp;quot;List patients whose mother was a diabetic&amp;quot;, we recall that it has the meaning representation:</Paragraph>
  </Section>
  <Section position="7" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(DISPLAY ~(SETOF X:PATIENTS
</SectionTitle>
    <Paragraph position="0"/>
    <Paragraph position="2"> Upon application to the SETOF expression, the algorithm first applies itself to the inner FORALL. The syntactic patterns of none of the pre-simplification transformations (2) - (4) are satisfied, so transformation (5) is applied right way to produce the NIKL concept:</Paragraph>
  </Section>
  <Section position="8" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(VALUERESTRICT (VRDIFF MOTHER PERSON)
DIABETIC)
</SectionTitle>
    <Paragraph position="0"> This is given to the NIKL classifier, which compares it to other concepts already i n the hierarchy. Since MOTHER has PERSON as its range already, (VRDIFF MOTHER PERSON) is just MOTHER again. The classifier thus computes that the concept specified above is a subconcept of PERSON - a PERSON such that his MOTHER was a DIABETIC. If this is not found to be equivalent to any pre-existing concept, the system assigns the concept a new name which no other concept has, say PERSON-I. The outcome of the simplification of the whole FORALL is then just the much simpler expression:</Paragraph>
  </Section>
  <Section position="9" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(PERSON-I X)
</SectionTitle>
    <Paragraph position="0"> The recursive simplification of the arguments to the SETOF is now completed, and the resulting expression is:</Paragraph>
  </Section>
  <Section position="10" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(DISPLAY 't(SETOF X:PATIENT
(PERSON-I X)))
</SectionTitle>
    <Paragraph position="0"> Transformations can now be applied to the SETOF  expression itself. The pre-simplification transformation (3) is found to apply, and a concept expressed by:</Paragraph>
  </Section>
  <Section position="11" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(CONJ PATIENT PERSON--I)
</SectionTitle>
    <Paragraph position="0"> is given to the classifier, which recognizes it as equivalent to the already existing concept PATIENT-WITH-DIABETIC-MOTHER. Since any concept can serve as a sort, the final simplification is:</Paragraph>
  </Section>
  <Section position="12" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(DISPLAY t(SETOF X:PATIENT-W\]TH-DIABETIC~THER))
</SectionTitle>
    <Paragraph position="0"> This is the very concept for which we have a rule, so the ERL translation is:</Paragraph>
  </Section>
  <Section position="13" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(PRINT FROM (SELECT FROM PATIENT
WHERE (EQ DIAMOTHER &amp;quot;YES&amp;quot;))
PATID)
</SectionTitle>
    <Paragraph position="0"> Suppose now that the semantic interpretation system assigned a different logical expression to represent the query &amp;quot;List patients whose mother was a diabetic&amp;quot;, in which the embedded quantification is existential instead of universal. This might actually be more in line with the number of the embedded noun. The meaning representation would now be: (disploy t(setof X:PATIENT (exists Y:PERSON (and (MOTHER X Y)</Paragraph>
  </Section>
  <Section position="14" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(DIABETIC Y)))
</SectionTitle>
    <Paragraph position="0"> The recursive application of the algorithm proceeds as before. Now, however, the pre-simplification transformation (2) may be applied to yield: (exists Y:DIABETIC (MOTHER X Y)) since a DIABETIC is already a PERSON. Transformation (6) can be applied if MOTHER is a &amp;quot;functional&amp;quot; role - mapping each and every person to exactly one mother. This can be checked by asking the NIKL system if a number restriction has been attached at the domain of the role, PERSON, specifying that it have both a minimum and a maximum of one. If the author of the domain model has provided this reasonable and perfectly true fact about motherhood, (6) can proceed to yield: (PAT I ENT-WI TH-D I ABET IC- MOTHER X) as in the preceding example.</Paragraph>
    <Paragraph position="1"> The role tightening phase This phase is quite simple. After the contraction phase has been run on the whole expression, a number of variables have had their sorts changed to tighter ones. This transformation sweeps through an expression and changes the roles in the expression on that basis. Thus: (IS) (R X Y) =&gt; (R' X Y) where $1 is the sort of X ond $2 is the sort of Y ond R' := (DOMAINDIFF (VRDIFF R $2) Sl) One can see that a use of the relation SEX, where the sort of the first argument is known to be DOCTOR, can readily be converted to a use the relation DOCTOR-SEX. Back conversion: going in the reverse direction There will be times when the simplification transformation will &amp;quot;overshoot&amp;quot;, creating and using new predicate letters which have not been seen before by classifying new data structures into the model to correspond to them. The use of such a new predicate letter can then be treated exactly as would its equivalent lambda-definition, which we can readily obtain by consulting the NIKL model. For example, a query about the sexes of leukemia victims may after simplification result in a rather strange role being created and entered into the hierarchy:</Paragraph>
    <Paragraph position="3"> This role is a direct descendant of PATIENT-SEX; its name is system generated. By the meaning-postulate of DOMAINDIFF given in section 3 above, it can be rewritten as the following lambda-abstract: (Iombdo (X Y) (and (PATIENT-SEX X Y) ( LEUKEM I A-PAT I ENT X) ) ) For PATIENT-SEX we of course have a translation rule as discussed in section 2. A rule for LEUKEMIA-PATIENT can be imagined as involving the DISEASE field of the PATIENTS table. At this point we can simply call the translation algorithm recursively, and it will come up with a translation:</Paragraph>
  </Section>
  <Section position="15" start_page="2238" end_page="2238" type="metho">
    <SectionTitle>
(PROJECT (SELECT FROM PATIENTS
WHERE (EQ DISEASE &amp;quot;LEUK&amp;quot;))
OVER PATID SEX)
</SectionTitle>
    <Paragraph position="0"> This supplies us with the needed rule. As a bonus, we can avoid having to recompute it later by simply attaching it to the role in the normal way. The similar computation of rules for complex concepts and roles which are already in the domain comes for free.</Paragraph>
  </Section>
class="xml-element"></Paper>