Discovering Relational Structure in Program Synthesis Problems with Analogical Reasoning

Abstract

Much recent progress in Genetic Programming (GP) can be ascribed to work in semantic GP, which facilitates program induction by considering program behaviour on individual fitness cases. It is therefore interesting to consider whether alternative decompositions of fitness cases might also provide useful information. The one we present here is motivated by work in analogical reasoning. So-called proportional analogies (gills are to fish as lungs are to mammals) have a hierarchical relational structure that can be captured using the formalism of Structural Information Theory. We show how proportional analogy problems can be solved with GP and, conversely, how analogical reasoning can be engaged in GP to provide for problem decomposition. The idea is to treat pairs of fitness cases as if they formed a proportional analogy problem, identify relational consistency between them, and use it to inform the search process.