A Complexity Based Approach for Solving Hofstadter's Analogies

Analogical reasoning is a central problem both for human cognition and for artificial learning. Many aspects of this problem remain unsolved, though, and analogical reasoning is still a difficult task for machines. In this paper, we consider the problem of analogical reasoning and assume that the relevance of a solution can be measured by the complexity of the analogy. This hypothesis is tested in a basic alphanumeric micro-world. In order to compute complexity, we present specifications for a prototype language used to describe analogies. A few elementary operators for this language are exposed, and their complexity is discussed both from a theoretical and practical point of view. We expose several alternative definitions of relevance in analogical reasoning and show how they are related to complexity.