Analogy and Bisimulation: A Comparison of Indurkhya's Cognitive Models and Heuristic-Driven Theory Projection
Lena Kurzen · 2005
The majority of formal approaches to analogy models analogies as structure preserving mappings from source to target domain. Bipin Indurkhya developed a formal theory of analogies and cognitive processes in general, where source and target are represented as concept networks, which are special kinds of algebras. The relation between them is modeled as an algebra as well. Another approach, which is also algebraic in nature, is heuristic-driven theory projection. It represents source and target domains as theories. Heuristic-driven theory projection is based on the idea that anti-unification can be used for modeling analogies. The analogical relation between source and target is induced by a heuristic algorithm that computes a third theory that is a generalization of source and target theories. In this thesis, the concepts of analogy and bisimulation, a notion expressing structural identity without being isomorphic, are brought together. The relations that model the connection between source and target in Indurkhya’s theory and in heuristic-driven theory projection are compared to each other and to bisimulation. Conditions are specified under which these relations are bisimulations.