An Algebraic Framework for Solving Proportional and Predictive Analogies

We present an approach to analogical reasoning which is inherently dependent on abstraction. While typical cognitive and AI models of analogy perform a direct mapping from objects of the base to objects of the target domain, our model performs mapping via abstraction. Abstraction is calculated as most specific generalization of the base and the target structure. In contrast to existing models, learning occurs as a side-effect of analogical reasoning. Our approach is based on the formally sound framework of anti-unification. It allows to deal with different kinds of analogy in a uniform way. After a description of the basic ideas of the approach, we will present examples from the domains of proportional and predictive analogy. Introduction The ability to use old information to explain new experiences can be considered as a core feature of human intelligence. Therefore, it is not astonishing that analogy is an active area of cognitive science research. There are numerous psychological studies and experiments as well as different computational models of analogical reasoning. The simplest form of analogical reasoning are proportional analogies of the form (A : B) :: (C : ?). They are studied in verbal settings (Lungs are to humans as gills are to [fish]), with geometric figures (Evans, 1968; O’Hara, 1992), and in string domains (Hofstadter et. al., 1995) (abc : abd :: kji : [kjj]). Proportional analogies can be formally characterized as isomorphism (Klix, 1993) (see Fig. 1). Analogy is not performed on the patterns themselves, but on descriptions of them. For each pattern , there must be found a description , such that !