186 user,and continually revised as the query is extended. No change is eeded as long as the target case remains one of the cases that are maximally similar to the current query As Figure 2 illustrates, attribute selection in inn aims to maxi- mise the number of cases dominated by the target case. The cases cur- rently dominated by the target case are shown in the lower half of the diagram. As indicated by the dashed arrows, there may be many dom inance relationships with respect to the current query, but iNn con- siders only cases that are dominated by the target case. For each of the remaining attributes. it uses the dominance criterion from Theo rem l to determine the number of cases that will be dominated by the target case if the preferred value of the attribute is the same as in the target case. It then selects the attribute that maximises the num ber of cases potentially dominated by the target case. If two or more attributes are equally promising according to this criterion, iNn uses the importance weights assigned to the case attributes as a second ary selection criterion. That is, it chooses the most important of the equally promising attributes. 3.4. Terminating the recommendation dialogue As we have shown in previous work, naive approaches to termination of recommendation dialogues such as stopping when the similarity of any case reaches a predefined threshold cannot guarantee that a bet- ter solution will not be found if the dialogue is allowed to continue (McSherry, 2003a). In fact, the only way to ensure that a more sim lar case(or another equally similar case) will not be found is to insist Maximally similar cases Target case Cases dominated by target case Figure 2. Attribute selection in iNN aims to maximise the number of cases dominate186 D. MCSHERRY user, and continually revised as the query is extended. No change is needed as long as the target case remains one of the cases that are maximally similar to the current query. As Figure 2 illustrates, attribute selection in iNN aims to maxi￾mise the number of cases dominated by the target case. The cases cur￾rently dominated by the target case are shown in the lower half of the diagram. As indicated by the dashed arrows, there may be many dom￾inance relationships with respect to the current query, but iNN con￾siders only cases that are dominated by the target case. For each of the remaining attributes, it uses the dominance criterion from Theo￾rem 1 to determine the number of cases that will be dominated by the target case if the preferred value of the attribute is the same as in the target case. It then selects the attribute that maximises the num￾ber of cases potentially dominated by the target case. If two or more attributes are equally promising according to this criterion, iNN uses the importance weights assigned to the case attributes as a second￾ary selection criterion. That is, it chooses the most important of the equally promising attributes. 3.4. Terminating the recommendation dialogue As we have shown in previous work, na¨ıve approaches to termination of recommendation dialogues such as stopping when the similarity of any case reaches a predefined threshold cannot guarantee that a bet￾ter solution will not be found if the dialogue is allowed to continue (McSherry, 2003a). In fact, the only way to ensure that a more simi￾lar case (or another equally similar case) will not be found is to insist Cases dominated by target case Target case Maximally similar cases Figure 2. Attribute selection in iNN aims to maximise the number of cases dominated by the target case