Logical proportions - Typology and roadmap

Publication Type:
Conference Proceeding
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2010, 6178 LNAI pp. 757 - 767
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Given a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators (a=b and a=b), or dissimilarity indicators (a=b and a=b) pertaining to the pair (a, b) to the ones associated with the pair (c, d). There are 120 distinct logical proportions. One of them models analogical proportions which correspond to statements of the form "a is to b as c is to d". The paper inventories the whole set of logical proportions by dividing it into 5 subfamilies according to what their logical proportions express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for (¬a,¬b, ¬c, ¬d)). Finally, the paper provides a discussion of the potential interest of logical proportions, which clearly have a cognitive appeal. © 2010 Springer-Verlag Berlin Heidelberg.
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