Interpolation and Extrapolation in Conceptual Spaces: A Case Study in the Music Domain

Abstract

In most knowledge representation settings, atomic properties correspond to natural language labels. Although these labels are usually taken to be primitive, automating some forms of commonsense inference requires background knowledge on the cognitive meaning of these labels. We consider two such forms of commonsense reasoning, which we refer to as interpolative and extrapolative reasoning. In both cases, rule-based knowledge is augmented with knowledge about the geometric representation of labels in a conceptual space. Specifically, to support interpolative reasoning, we need to know which labels are conceptually between which other labels, considering that intermediary conditions tend to lead to intermediary conclusions. Extrapolative reasoning is based on information about the direction of change that is needed when replacing one label by another, taking the view that parallel changes in the conditions of rules tend to lead to parallel changes in the conclusions. In this paper, we propose a practical method to acquire such knowledge about the conceptual spaces representation of labels. We illustrate the method in the domain of music genres, starting from meta-data that was obtained from the music recommendation website last.fm.