From analogical proportions in lattices to proportional analogies in formal concepts
Laurent Miclet, Nelly Barbot, Henri Prade · Frontiers in artificial intelligence and applications · 2014
The paper provides an attempt at bridging formal concept analysis and the modeling of analogical proportions (i.e., statements of the form “a is to b as c is to d”). A suitable definition for analogical proportions in non distributive lattices is proposed and then applied to concept lattices. This enables us to compute what we call proportional analogies that establish analogies on a proportional basis between pairs (a, b) and (c, d) when a and c belong to a domain and b and d to another domain (as in “Moby Dick is to Herman Melville as Alice in Wonderland is to Lewis Carroll”).