# QB4 MobOLAP: A Vocabulary Extension for Mobility OLAP on the Semantic Web
## 4 Results and Discussion
### Defining Spatiotemporally Enhanced MD Data in QB4 MobOLAP  
Spatial Attributes. Spatial attributes are specified on a domain level. Each attribute with a geometry domain (_sa: domgeo_\(\in A\)) is a member of the geo:Geometry class and is referred to as a spatial attribute, which is represented in the cube schema \(CS\) as (sa rdf:type qb:AttributeProperty; rdfs:domain geo:Geometry). In the instances, each spatial attribute type (point, polygon, line, etc.) is assigned using the predicate rdfs:range. Example 4  
#Attributes  
ffb:plantationKey rdf:type qb4o:levelAttribute;  
qb4o:inLevel ffb:plantation;  
rdfs:range xsd:Integer. ffb:plantationName rdf:type qb4o:levelAttribute;  
qb4o:inLevel ffb:plantation;  
rdfs:range ssd:String. ffb:plantationGeo rdf:type qb4o:levelAttribute;  
qb4o:inLevel ffb:plantation;  
rdfs:subPropertyOf geo:Geometry;  
rdfs:range geo:wkHateral;  
rdfs:domain geo:Polygon;  
rdfs:subClassOf geo:SpatialObject;  
Spatial Hierarchies. Two or more spatial levels \(l_{\text{s}}\in H\). The spatial hierarchy step describes a roll-up relation between the spatial levels. QB4 SOLAP introduces topological relations, \(T_{\text{r}}\), in addition to cardinalities in the roll-up relation that are encoded as \(R=(L_{\text{c}},\ L_{\text{p}},\ c,\ T_{\text{r}})\) for the spatial hierarchy steps. Let \(t_{\text{shs}}\in T\) be a set of triples to represent a hierarchical step for spatial levels in hierarchies, which is given with a blank node: \(\_sh_{\text{hs}}\in B\) and encoded as (\(\_shsh_{\text{hs}}\) rdf:type qb4o:HierarchyStep; qb4o:childLevel slhc; qb4o:parentLevel slhp; qb4o:cardinality c;qb4 so:hasTopologicalRelation Tr) where \(slhci\in Lc\), \(slhpi\in Lp\). For example, a spatial hierarchy is \"geography\", which should have spatial levels (e.g., FruitCollectionPoint, Block, Afdeling, and Plantation) with the roll-up relation \(Rh=\) (Block, Afdeling, many-to-one, within), which also specifies that the child-level Afdeling is \"within\" the parent level Plantation. Spatial Dimensions. Dimensions are considered spatial if they contain at least one spatial hierarchy. More than one dimension can share the same spatial hierarchy and spatial levels as that hierarchy. Spatial Measures. A Spatial measure \(sm\in M\) is specified by a set of triples \(t_{\text{sm}}\in T\) and represented as (sm rdf:type qb:MeasureProperty; rdfs:subPropertyOf sdmx-measure: obsValue; rdfs:domain geo:Geometry) in the cube schema \(CS\). Spatial measures are represented by a geometry that uses geometry serialization standards in OGC schemas. For example, a spatial measure is a trajectory that contains a list of coordinates of locations, which is given as a line geometry type and is associated with an observational fact of the trajectory of delivery. Mobility Measures. A mobility measure \(mm\in M\) is specified in the cube schema CS by a set of triples \(t_{\text{mm}}\in T\) and encoded as (mm rdf:type qb:MeasureProperty; rdfs:subPropertyOf sdmx-measure:obsValue; rdfs:domain qb4 mob:MobilityBase/MobilityGeometry). The class of the numeric value is given with the property rdfs:domain, and rdfs:range assigns the values from the class qb4 mob:MobilityBase/mobilityPoint, i.e., the temporal integer, temporal float, temporal point, temporal polygon, etc., at the instance level. Mobility measures are represented by a mobility base/geometry. These mobility measures use schema extension of OGC schemas with temporal natures that change over time. Mobility Facts. Mobility facts \(F_{\text{m}}\) have mobility/spatiotemporal natures that are related across several dimensions, either spatial or temporal. The mobility fact cube has mobility measures (\(m_{\text{m}}\)), as its members make it possible to aggregate mobility measures with the aggregation functions \(M_{\text{agg}}\).