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A Qualitative Model to Reason about Object Rotations (QOR) applied to solve the Cube Comparison Test (CCT)

Zoe Falomir

TL;DR

The paper tackles modeling 3D object rotations and their effects on side locations and orientations to automate reasoning for the Cube Comparison Test (CCT). It introduces Qualitative Object Rotations (QOR), built from a Qualitative Object Descriptor (QOD) and a Rotation Reference System, and encodes rotation-induced transitions via Conceptual Neighborhood Graphs. An algorithm solves the CCT by counting repeated features ($R \in \{0,1,2,3\}$) and tracing rotation paths in $CNG_{RLO}$ to ensure feasible location/orientation changes and orientation consistency. The approach delivers a transparent, explainable qualitative reasoning framework with applicability to cognitive robotics, human-computer interaction, and educational tools for training spatial skills. It extends qualitative spatial reasoning methods to dynamic 3D object manipulation and provides a structured pathway for assessing object identity across perspectives.

Abstract

This paper presents a Qualitative model for Reasoning about Object Rotations (QOR) which is applied to solve the Cube Comparison Test (CCT) by Ekstrom et al. (1976). A conceptual neighborhood graph relating the Rotation movement to the Location change and the Orientation change (CNGRLO) of the features on the cube sides has been built and it produces composition tables to calculate inferences for reasoning about rotations.

A Qualitative Model to Reason about Object Rotations (QOR) applied to solve the Cube Comparison Test (CCT)

TL;DR

The paper tackles modeling 3D object rotations and their effects on side locations and orientations to automate reasoning for the Cube Comparison Test (CCT). It introduces Qualitative Object Rotations (QOR), built from a Qualitative Object Descriptor (QOD) and a Rotation Reference System, and encodes rotation-induced transitions via Conceptual Neighborhood Graphs. An algorithm solves the CCT by counting repeated features () and tracing rotation paths in to ensure feasible location/orientation changes and orientation consistency. The approach delivers a transparent, explainable qualitative reasoning framework with applicability to cognitive robotics, human-computer interaction, and educational tools for training spatial skills. It extends qualitative spatial reasoning methods to dynamic 3D object manipulation and provides a structured pathway for assessing object identity across perspectives.

Abstract

This paper presents a Qualitative model for Reasoning about Object Rotations (QOR) which is applied to solve the Cube Comparison Test (CCT) by Ekstrom et al. (1976). A conceptual neighborhood graph relating the Rotation movement to the Location change and the Orientation change (CNGRLO) of the features on the cube sides has been built and it produces composition tables to calculate inferences for reasoning about rotations.
Paper Structure (8 sections, 3 equations, 8 figures, 4 tables)

This paper contains 8 sections, 3 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The Cube Comparison Test (CCT)
  3. The Qualitative Model of Object Rotations
  4. The Qualitative Object Descriptor (QOD)
  5. Rotations in QODs (QOR$_{RS}$)
  6. Rotations related to Location and Orientation Change
  7. Solving the Cube Comparison Test (CCT)
  8. Conclusions and Future Work

Figures (8)

  • Figure 1: Example question and instructions given in the Cube Comparison Test (CCT) from the Manual for Kit of Factor-Referenced Cognitive Tests by Ekstrom76.
  • Figure 2: Example of an object view described by the QOR model.
  • Figure 3: Perspective front-right-up.
  • Figure 4: Example of the same cube view in \ref{['fig:vO']} but rotated, discovering a new feature (T) and changing the orientations of two common features (G and B).
  • Figure 5: Operators for QOR: rotating objects depending on 3 axes in two possible directions.
  • ...and 3 more figures