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cs.AI2026
A Generalized Parallelogram Rule for Proportional Analogies on Riemannian Manifolds
Pierre-Alexandre Murena, Marcelo Hartmann
Analogies are quaternary relations of the form "a is to b as c is to d", usually denoted a : b :: c : d. This notion is formalized in particular with the notion of proportional ana…
cs.AI2026
Proportional Analogies on Probability Distributions via Bayesian Updating
Pierre-Alexandre Murena
Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiom…
cs.AI2022
Measuring the Feasibility of Analogical Transfer using Complexity
Pierre-Alexandre Murena
Analogies are 4-ary relations of the form "A is to B as C is to D". While focus has been mostly on how to solve an analogy, i.e. how to find correct values of D given A, B and C, l…