Empirically test the relation-dependent scaling hypothesis for human temporal grading

Determine whether human temporal grading uses the relation-dependent yardsticks predicted by the probabilistic Allen algebra: combined object extents for separation relations, the container extent for containment relations, and salience- or event-kind-dependent scales when both objects collapse to points.

Background

The paper derives a proposed scaling structure for graded temporal relations. For separation, the relevant margin is the temporal gap normalized by the combined uncertainty and influenced symmetrically by the two object extents. For containment, the proposed yardstick is the extent of the containing interval, while the contained object's extent enters with the opposite effect. When both objects degenerate to points, no intrinsic interval extent remains, so the paper hypothesizes that a scale related to event kind or salience must be supplied externally, potentially on a logarithmic axis.

The authors state that these geometric claims require behavioral validation. Such experiments should independently vary object extents in separation and containment configurations, control or match salience, and determine whether human judgments exhibit the predicted summed-extents, container-minus-contained, boundary-pinning, and salience-dependent effects.