Generating Numerical Approximations

We describe a computational model for planning phrases like “more than a quarter” and “25.9 per cent” which describe proportions at different levels of precision. The model lays out the key choices in planning a numerical description, using formal definitions of mathematical form (e.g., the distinction between fractions and percentages) and roundness adapted from earlier studies. The task is modeled as a constraint satisfaction problem, with solutions subsequently ranked by preferences (e.g., for roundness). Detailed constraints are based on a corpus of numerical expressions collected in the NUMGEN project,1 and evaluated through empirical studies in which subjects were asked to produce (or complete) numerical expressions in specified contexts.