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<Paper uid="W05-1606">
  <Title>Generating Referential Descriptions Under Conditions of Uncertainty</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Representing Uncertainties
</SectionTitle>
    <Paragraph position="0"> Basically, our model of uncertainty combines the three kinds of uncertainty described in the previous section. Each of them is expressed in terms of a probability, associated with a triple consisting of an object, an attribute applicable to that object, and the value ascribed to this pair. The following probabilities each express the likelihood that the user recognizes a description correctly from the perspectives of: pK The user is acquainted with the terms mentioned pP The user can perceive the properties uttered pA The user agrees to the applicability of the terms used In order to identify an intended referent successfully, all three factors must be assessed positively, so that the probability of recognition p becomes the product of these three probabilities. Since the individual properties refer to factors outside the scope of proper generation, we only deal with p in the scope of this paper, although it is clear that this assessment requires contributions from several sources.</Paragraph>
    <Paragraph position="1"> The concept of using individual probabilities to represent manifestations of uncertainty is not only simple, it also fits to knowledge sources where data about these probabilities could be found. For example, user models, the potential sources for assessing pK, typically assign assessments to user capabilities on the basis of belief networks. Similar considerations hold for representations of vague properties, which fall under the concept of term agreement. These properties can be modeled by fuzzy logic systems [Zadeh 1984, 1996], which allow for an interpretation in terms of a single probability value, representing the likelihood that a precise value is perceived as a given vague term.</Paragraph>
    <Paragraph position="2"> The association of a probability with the applicability of a descriptor to an object not only expresses the somehow direct likelihood of success of this task, but the application of this likelihood to several candidate objects also gives an indication of the likelihood of success of the overall identification goal. If a descriptor is assumed to be associated with several candidate objects by the audience, with certain degrees typically different among these objects, several cases can be distinguished: (1) correct identification, where the audience relates the description only to those objects to which this descriptor indeed applies, (2) misinterpretation, where none of these objects, but others are associated with the descriptor by the audience, (3) ambiguity, which is a combination of (1) and (2), and, finally, (4) the case of an uninterpretable description, where the audience does not relate the descriptor to any of the candidate objects. In the last case, people are known to make an attempt to repair their unsuccessful interpretation, since they assume that the expression communicated is indeed intended to refer to some object or objects in the domain of discourse, according to the work by Goodman. In order to simulate the effect of this behavior, we compute the probability of the occurrence of an uninterpretable description, which we call the repair factor, and we increase the probability of identification of the candidate objects (which we call our repair mechanism), based on the amount of the repair factor and the context of these objects in the overall identification task.</Paragraph>
    <Paragraph position="4"> f(j,m,n) recursively enumerates all combinations of m out of n elements (here: natural numbers 1 ... n) and returns the j-th combination as a set of numbers M={i1,...,im} with 1[?]ik[?]n</Paragraph>
    <Paragraph position="6"> In concrete terms, if we have n objects for which a descriptor is recognized with probability pi for object i, the probability that none of the objects is recognized by a referring expression built from that descriptor is P(1-pi), (1 [?] i [?] n).</Paragraph>
    <Paragraph position="7"> Although this number tends to be small if there are several objects to which the description matches with some reasonable degree of confidence, the associated need for invoking a repair mechanism becomes increasingly urgent when further descriptors are added to the description built so far, as well as when the task is to identify multiple referents rather than a single one. For the case of 2 objects, the need for invoking a repair mechanism can be quantified by the repair factor 2Pi=1,n(1-pi)+Si=1,n(piPj=1,n(j[?]i)(1-pj)). The general case, if needed, gets increasingly complex, as illustrated in Figure 1, for k objects to be identified, out of n candidates (k [?] n).</Paragraph>
    <Paragraph position="8"> Thus, for the likelihood of recognition failure, a mechanism is required that simulates identification repair under these conditions. Apart from the likelihood of failure, repair should be guided by potential confusability of objects in view of some given descriptor. Hence, while we think it is virtually impossible to confuse an animal and a piece of equipment, at least under any reasonable conditions of visibility, we assume that objects of some degree of appearance similarity (size and shape) may potentially be confused with each other. Hence, we consider a potentially confusable object a candidate for being interpreted as an intended referent in case a repair of a reference failure is required. Confusion in this sense may be interpreted in two ways: from the perspective of the speaker, those objects are candidates which the speaker thinks the hearer could confuse. From the hearers perspective, those objects are candidates which the hearer thinks the speaker might have confused in producing a badly interpretable description. Since the latter constellation corresponds to the situation present for repair attempts, we model potential candidates quasi &amp;quot;objectively&amp;quot; by incorporating annotations in the knowledge base. The dependency of user capabilities as assessed by a user model influences these assessments indirectly through the probability of recognition attributed to the user for each descriptor-object pair.</Paragraph>
    <Paragraph position="9"> Determine probability of identification (D, k, O1, ..., On) O1, ..., Om Objects to which descriptor D applies Om+1, ..., On Objects to which repair with D is applicable pi, ..., pm Probability that D is recognized for Oi Objects ordered along degrees of recognition confidence: [?]i,j(1 [?] i, j [?] m): (pi &gt; pj) - (i &gt; j)  that do not apply to it, but which could somehow be perceived as holding for this object. The potentially large amount of data created this way can be significantly reduced by making use of inheritance. For example, one can state that blue and purple (physical) objects can be confused, by making annotations about confusability with blue for purple objects, and vice-versa. This annotation is then inherited to all entities that are specializations of (physical) objects.</Paragraph>
    <Paragraph position="10"> The proper repair is then simulated by collecting all candidates to which the descriptor in question could arguably apply, and by assigning these candidates a probability of identification through repair, according to the repair factor, as assessed above. There are two kinds of candidates: (1) those to which the descriptor is recognized with some probability, and (2) those to which it could apply with some relaxation, that is, which contains a suitable confusability annotation. The repair factor, which is computed according to the schema in Figure 1, is then evenly distributed among these two sets of candidates, provided the added probabilities of recognition and repair do not get greater than 1 for some object; this can only be the case if the number of objects to identify is close to the number of candidates. In such a case, the extra amount is distributed recursively among the remaining candidates, always respecting the upper limit of 1.</Paragraph>
    <Paragraph position="11"> If the number of objects to identify even exceeds the number of candidates, the effect of the repair mechanism results in a modification of the number of objects to identify, reducing it to the number of available candidates. The computation of the probability of identification through repair is illustrated in Figure 2. Three examples in Figure 3 illustrate the effect of the repair mechanism in quantitative terms. They emphasize the relation between expectations about the number of objects to be identified and probabilities of identification.</Paragraph>
    <Paragraph position="12"> For k objects to be identified out of n, judging identification by descriptor D, which may involve repair measures (D applies to m out of these n with probabilities pi,...,pm)</Paragraph>
    <Paragraph position="14"> Specifically, the increasing contributions of the repair facility are shown, which will be even more pronounced with several attributes associated with limited recognition expectations. We will see this effect in context with building descriptor combination in the next section, as well as in the detailed exposition of an example in Appendix II.</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 Identifiability of Descriptor Compositions
</SectionTitle>
    <Paragraph position="0"> Since a single descriptor is rarely sufficient for identifying one or several objects in scenarios of interesting complexity, boolean compositions of descriptors are generated for this purpose, conjunctions being required for building identifying expressions for single objects. Their probability of recognition is a simple extension of the case of single descriptors. If pi is the probability of recognition of descriptor Di for some object O, an expression consisting of several Di (i=1,pn) is identified with O through recognition if all Di are attributed to O. The probability of this coincidence amounts to the product of all probabilities Ppi (i=1,pn).</Paragraph>
    <Paragraph position="1"> The probability of identification through repair is computed by distributing the repair factor R(k,P1,...,Pm), where each Pj=Ppji (j=1,m;i=1,pn), among all objects qualifying for the repair measure. While this distribution is an equal one for the case of a single descriptor, apart from using the upper limit of 1 for the total probability, such an even distribution would not do full justice here. We propose to distribute the likelihood proportionally to the probabilities of recognition for each descriptor, which makes repair more likely applicable to those objects which are also more likely to be identified anyway. In order to perform this operation properly, &amp;quot;average&amp;quot; probabilities (ap) for only reparable descriptors must be estimated. Moreover, we want to favor repairs for objects which require fewer &amp;quot;average&amp;quot; probabilities for this computation, by incorporating a &amp;quot;scale-down factor&amp;quot; (sdf) for each additional repair. The computation schema is given in Figure 4. For concrete computations, we choose 0.5 for both factors ap and sdf - see the examples in Figure 5.</Paragraph>
    <Paragraph position="2"> The first one demonstrates the partitioning of the repair factor according to the number of attributes which require repair. Specifically, the first three objects get the same share of the repair factor, while the fourth object gets only half of it, since its identification is the only one which requires  repair regarding two descriptors. The second example features the impact of multiple intended referents on the repair factor, which increases the probabilities of identification substantially. The last example illustrates the compensative effect between comparably low probabilities of recognition and higher ones in connection with the requirement of using the repair facility. Specifically, this example demonstrates that the probability of identification for an object (the second one) that is only identifiable through the repair mechanism can even become higher than the probability of identification for an object (the second one) that does not require repair for being identified. However, such an effect is only possible in the context of descriptors applicable with some degree of confidence to both candidates, but strongly favoring the object whose identification relies on the repair mechanism due to mismatch with another descriptor. This is the most critical effect in choosing descriptors.</Paragraph>
    <Paragraph position="3"> The incorproation of disjunctions and negations is more local, since this extension only generalizes the probability of recognition of a single property. This is because these operators appear only in embedded boolean combinations [van Deemter 2002], which are the basis for building larger varieties of expressions [Horacek 2004]. For disjunctions of two descriptors with associated probabilities p1 and p2, the joint probability amounts to p1+p2-p1p2, assuming independence, which is quite normal for descriptors originating from For k objects to be identified out of n, judging identification by np descriptors D, at least repair possible for all (Dj applies to object i with probability pji, [?]i[?]m: pji &gt; 0)</Paragraph>
    <Paragraph position="5"> distinct properties. For some properties, prominently those associated with vagueness, building disjunctions of descriptors originating from the same property may be beneficial. For example, disjunctions of similar colors or shapes may reduce the uncertainty through combining the identifiability of both. A simple way to model this constellation is by assigning probabilities to the set of applicable values so that their sum does not exceed 1, thereby modeling exclusion of the co-occurrence of more than one value.</Paragraph>
    <Paragraph position="6"> Consequently, the associated probabilities can simply be added. Propagation of the &amp;quot;confusable&amp;quot; annotation is treated similarly - if at least one of the descriptors is marked as &amp;quot;confusable&amp;quot;, this also holds for the disjunction. For dealing with negation, the probability of identification is simply inverted (1-p). The treatment of the &amp;quot;confusable&amp;quot; annotation, however, is a bit problematic. The invertion operation needs modification through anticipating the amount of the repair factor, but this cannot be done locally. Therefore, this factor, rf, must be estimated in advance. For concrete computations we use a value of 0.1, so that !p for a &amp;quot;confusable&amp;quot; p amounts to 0.9.</Paragraph>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 An Algorithm Incorporating Uncertainties
</SectionTitle>
    <Paragraph position="0"> In this section, we describe extensions to the algorithm by Dale and Reiter [1995] that take into account the measures addressing uncertainty introduced in previous sections. This reference algorithm takes an intended referent r (the generalization to several referents is straightforward), the attributes P that describe r, and a contrast set C, and incrementally builds an identifying description L, if possible. The algorithm assumes an environment with three interface functions: BasicLevelValue, accessing basic level categories of objects [Rosch 1978], MoreSpecificValue for accessing incrementally specialized values of an attribute according to a taxonomic hierarchy, and UserKnows for judging whether the user is familiar with the attribute value of an object.</Paragraph>
    <Paragraph position="1"> The algorithm basically iterates over the attributes P, according to some predetermined ordering which reflects preferences in the domain of application. For each attribute in P, a value assumed to be known to the user is determined, so that this value describes the intended referent and rules out at least one potential distractor which is still in the contrast set C in the iteration step considered. If such a value can be found, a pair consisting of the attribute and this value is included in the identifying description L. This step is repeated until the list P is exhausted or a distinguishing description is found, that is, the contrast set C is empty.</Paragraph>
    <Paragraph position="2"> Unless the distinguishing description L does not contain a descriptor expressible as a head noun, such a descriptor is added. Choosing the value of an attribute is done by an embedded iteration. It starts with the basic level value attributed to r, after which more specific values also attributed to r and assumed to be known to the user are tested for their discriminatory power. Finally, the least specific value that excludes the largest number of potential distractors and is known to the user is chosen. The schema of this procedure is given in Appendix I. The only modification we have done to the original version is the result of L as a non-distinguishing description in case of identification failure.</Paragraph>
    <Paragraph position="3"> The algorithm by Dale and Reiter contains the principal operations that also other algorithms for generating referring expressions apply. The extension to boolean combinations of descriptors by van Deemter is essentially realized as an iteration around the Dale and Reiter algorithm, through building increasingly complex combinations, which other control regimes generate and maintain more effectively.</Paragraph>
    <Paragraph position="4"> In order to control effects of facilities dealing with uncertainty, the extended algorithm has four control parameters: * pmin, the minimal probability of recognition required for an attribute-value pair applicable to the intended referent, to justify its inclusion in the description, * [?]p1, the minimal improvement in terms of probability of identification of the intended referent over a potential distractor obtained through an additional attribute-value pair, * [?]p2, the minimal preference in terms of probability of identification of the intended referent over all potential distractors obtained through a description, and * Complexity-limit, an upper bound on the number of descriptors collected in the distinguishing description.</Paragraph>
    <Paragraph position="5"> In order to incorporate our concepts of representing uncertainty in this algorithm, we have to replace the interface functions which access crisp data and we must modify yes-no decisions. These enhancements concern: * the decision about whether a descriptor excludes a potential distractor (in the function RulesOut), * the choice of a value for an attribute (in the function FindBestvalue), and * the termination of the overall procedure (in the function MakeReferringExpression) Modifications of the reference algorithm are given in detail in the extended version in Appendix I - some lines are marked by labels [Ni] for references from the text.</Paragraph>
    <Paragraph position="6"> Expressions of the form pr(r,L) compute the probability of identification of referent r through the description L, according to the schema described in the previous sections.</Paragraph>
    <Paragraph position="7"> Under conditions of uncertainty, determining whether a descriptor excludes a potential distractor may become a proper decision rather than a mere computation. A clear-cut case is only present if the repair facility is not applicable to one of the members of the contrast set, so that its associated probability of identification amounts to 0. This condition replaces the criterion that the user must know that this descriptor does not apply to some potential distractor in the function RulesOut [N7]. However, it would be a rather restrictive strategy to accept only those descriptors which definitely exclude a potential distractor. In fact, none of the descriptors that make up the example in Appendix II yield such a crisp discrimination. In addition to that, a descriptor is also valuable if it contributes to a better identification of the intended referent by increasing the difference to a potential distractor in the associated probabilities of identification by a significant margin ([?]p1). This criterion is added to the crisp criterion described above, encapsulated in the function Dominate [N8], which is used for this decision instead of the function RulesOut [N2]. The idea is that subsequently chosen descriptors have comparable effects on the identification of some of the other potential distractors, so that the intended referent ultimately gains over all of them. The significance of this margin must be tuned in such a way that the gain over some potential distractors is not outweighted by a loss over some other potential distractors.</Paragraph>
    <Paragraph position="8"> The suitability of a value for an attribute depends on two factors associated with uncertainty: the probability of recognition associated with that value for the present user, and the effect of this value on excluding elements from the set of potential distractors. These two factors have adverse effects: while a more specific value has the potential of excluding an increasing number of potential distractors, its probability of recognition when applied to the intended referent may be lower than that of a less specific value. Consequently, it is not necessarily the case that an improved discriminatory power leads to a better overall effect. Hence, the choice of a value requires a minimal probability of recognition (pmin, [N6]), and calls to Dominate replace calls to RulesOut. Additional variants of descriptors can be generated by enhancing the interface function MoreSpecificValue, also building disjunctions of values excluding each other, to cover cases described at the end of Section 4, that is, building disjunctions of descriptors by composing descriptors (possibly vague ones) that cover adjacent value ranges.</Paragraph>
    <Paragraph position="9"> The third factor, the termination criterion, is adapted to uncertainties by enhancing it in two ways: (1) a complexity limit is applied to the specifications in the description L [N3]; while this cut-off may serve practical considerations also without conditions of uncertainty (for a partitioning into sequences of descriptions [Horacek 2004]), it gains on relevance in uncertain environments. (2) a certain degree of being Dominant in the probability of identification over all potential distractors is considered sufficient ([?]p2, [N4]) rather than requiring the ultimate exclusion of all potential distractors. Finally, the conditions under which descriptors are selected, give rise to an optional optimization step. The prerequisite for this step is the distinction between descriptors which definitively exclude at least one potential distractor (Lro in the extended algorithm, [N1]) and others which only affect their associated probabilities of identification, but do not make them 0. Then all subsets of the description built which contain at least Lro are examined [N5] whether they yield a better preference over all potential distractors in terms of their probabilities of identification [N9]. Through this measure, an early chosen descriptor with a probability of identification lower for the intended referent than for some potential distractors can finally be discarded, provided the discriminating effect on other potential distractors is also achieved by later chosen descriptors. In the example in Appendix II, all descriptors are categorized as optional ones, but for the one expressing the head noun which is precisely the reason why it is not optional.</Paragraph>
    <Paragraph position="10"> Altogether, the algorithm selects descriptors which either exclude some potential distractors definitively, makes some of them rely on the repair mechanism, or simply increases the probability of identification of the intended referent considerably in comparison to elements of the contrast set.</Paragraph>
    <Paragraph position="11"> While this selection process works reasonably in most cases, it may turn out as problematic when several of the descriptors chosen are associated with limited probabilities of recognition for the intended referent in comparison to potential distractors not completely excluded. As a consequence, these potential distractors may be judged superior in terms of the probability of identification even though they rely on the repair mechanism (see example 3 in Figure 5).</Paragraph>
    <Paragraph position="12"> This risk can be circumvented by using a relatively high pmin parameter, but this measure may easily lead to the exclusion of an otherwise beneficial descriptor under normal conditions. An improvement can be obtained by the call to the procedure Optimize. If one of the first two descriptors used in example 3 in Figure 5 does not definitively exclude a potential distractor, the procedure Optimize tests descriptor combinations without it, and one of those may yield a better result - see also the example in Appendix II. A possible variations would be to allow just a single violation of the pmin restriction, for a descriptor with very good discriminatory power.</Paragraph>
    <Paragraph position="13"> So far, we have only elaborated changes for incorporating uncertainty concepts to the reference algorithm per se. Handling boolean combinations of descriptors through applying the reference algorithm to increasingly complex combinations also works with uncertainties, since all computations required are defined. More difficulties arise with ambitious control regimes, which rely on cut-off techniques, in addition to the complexity cut-off, such as dominance and value cut-offs, as introduced in [Horacek 2004]. A complexity cut-off is already included in the extended reference algorithm. The two other cut-offs can be generalized, but this is likely to be associated with a significant loss of efficiency. In order for a descriptor to dominate another one, the dominating one must not only exclude all potential distractors that its competitor does, but it must also favor the intended referents over all potential distractors in terms of the associated probabilities of identification - this requirement reduces the application frequency of this cut-off considerably. A value cut-off, in turn, is applicable to a partial solution if a solution has already been found, and there are no descriptor combinations untested for the partial solution which may yield a solution with less complex specifications. This condition can also be met in the environment associated with uncertainties. In this environment, however, there is another factor that has an impact on the quality of the solution, that is the probability of identification, which cannot be assessed prior to actually choosing a descriptor and testing its effects.</Paragraph>
  </Section>
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