Picking the one that does not fit - A matter of logical proportions - Archive ouverte HAL Access content directly
Conference Papers Year : 2013

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).
Fichier principal
Vignette du fichier
prade_12867.pdf (245.18 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01197281 , version 1 (11-09-2015)




Henri Prade, Gilles Richard. Picking the one that does not fit - A matter of logical proportions. 8th European Society For Fuzzy Logic And Technology Conference (EUSFLAT 2013), Sep 2013, Milano, Italy. pp.392-399, ⟨10.2991/eusflat.2013.61⟩. ⟨hal-01197281⟩
100 View
109 Download



Gmail Mastodon Facebook X LinkedIn More