More than just One Box

To support the representation of furniture assembly, we need an ontology to describe the shapes of integrated three-dimensional objects. There are few existing formal axiomatizations in this domain. MWorld Ontology, with nine modules, is a first order logic ontology proposed in this paper which allows the description of topological shapes composed of boxsets, boxes, surfaces, edges and points. We introduced boxset as the class for the shapes of integrated three-dimensional objects, componentOf as the proper parthood relation between the components and the whole, as well as semicomplements to capture the relationship between the disjoint components of the same whole. We proposed terms for coincident shapes in adjacent components: joint point, joint edge and joint surface. We reused CardWorld and BoxWorld, as an extension, we introduced featureOf as a new parthood relation to represent the relationship between substructure or basic shapes and their superstructure. As such, these theories can represent aspects of shapes with different dimensions following multidimensional and mereological pluralism approaches. All concepts and relationships are axiomatized and demonstrated with examples.