Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)

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

Authors
Henri Prade, Gilles Richard
Corresponding Author
Henri Prade
Available Online August 2013.
DOI
https://doi.org/10.2991/eusflat.2013.61How to use a DOI?
Keywords
analogy dissimilarity fuzzy logic
Abstract

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).

Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
Series
Advances in Intelligent Systems Research
Publication Date
August 2013
ISBN
978-90786-77-78-9
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2013.61How to use a DOI?
Copyright
© 2013, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Henri Prade
AU  - Gilles Richard
PY  - 2013/08
DA  - 2013/08
TI  - Picking the one that does not fit - A matter of logical proportions
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 432
EP  - 439
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.61
DO  - https://doi.org/10.2991/eusflat.2013.61
ID  - Prade2013/08
ER  -