Picking the one that does not fit - A matter of logical proportions

Quiz or tests about reasoning capabilities often pertain to the perception of similarity and dissimilarity between situations. Thus, one may be asked to complete a series of entities A, B, C by an appropriate X, or to pick the one that does not fit in a list. It has been shown that the first problem can receive a solution by solving analogical proportion equations between the representations of the entities in a logical setting, where we assume that X should be such that A is to B as C is to X. In this paper, we focus on the second problem, and we show that it can be properly handled by means of heterogeneous proportions that are the logical dual of the homogeneous proportions involved in the modeling of analogical proportions and related proportions. Thus, the formal setting of logical proportions, to which homogeneous and heterogeneous proportions belong, provides an appropriate framework for handling the two problems in a coherent way. As it already exists for homogeneous proportions, a particular multiple-valued logic extension of heterogeneous proportions is discussed (indeed being an intruder in a group may be a matter of degree).