# QB4 MobOLAP: A Vocabulary Extension for Mobility OLAP on the Semantic Web
## 4 Results and Discussion
### Multidimensional Data Cube Definition in QB4 MobOLAP  
The QB4 OLAP vocabulary modeled a multidimensional data cube in RDF terms. Multidimensional models are typically interpreted as data cubes, with cube cells corresponding to observational facts that are central to MD analysis. Facts have a set of properties called measures, which have aggregate functions that can be defined. To provide alternative analytic viewpoints, a data cube has \(n\) dimensions (with the attribute of contextual information) on a multidimensional space, where each dimension might have hierarchies with levels. Users can aggregate measures (of facts) at multiple levels of detail by using levels (of dimensions) (also known as granularity). Dimensions and facts are tied to the structure to assist this analysis at various detail levels. Levels also include attributes that describe the basic features of the members of the level. These MD concepts (cube elements) and their roles and relationships are annotated at the schema level in RDF triple format using the QB4 OLAP Vocabulary. Schema level (RDF) cube elements correspond to tables and columns (of tables) in an MD. Fact members with measure values and level members with attribute values are instance-level MD concepts annotated at the instance level with QB4 MobOLAP Vocabulary. These instance level (RDF) cube elements correspond to the actual data rows/records annotated in triple format with QB4 MobOLAP. An RDF triple \(t\) is made up of three parts: the subject (\(s\)), the predicate (\(p\)), and the object (\(o\)), which is defined as triple (\(s\),\(p\),\(o\)) \(t=\) (\(I\cup Bn\)) \(\times\)\(I\) (\(I\cup Bn\)\(\cup\)\(L\)), where \(I\) is the set of IRIs, \(Bn\) is the set of blank nodes, and L is the set of literals. The Cube Schema (\(CS\)), with element \(x\) defined as \(CS(x)\) (\(I\cup Bn\)\(\cup\)\(L\)), yields a set of triples \(T\) and is denoted by (x rdf:type ex:Property). MD Schema. A data structure definition (DSD) contains information about the schema of a data set (i.e., a cube, an instance of the class qb:DataSet). The DSD can be applied to a variety of data sets. A data set's DSD includes dimensions, levels, measures, and attributes, in addition to component properties. As \(CS\) = DSD, the DSD is defined by a conceptual MD cube schema \(CS\), which includes a collection of dimension types \(D\), a collection of measures \(M\), and a collection of fact types as \(CS\) = (\(D\), \(M\), \(F\)). The following definitions apply to the cube schema elements:  
Figure 6: QB4 MobOLAP Vocabulary. Attributes. An attribute \(a\in A=\{a_{1},a_{2},\ldots,a_{n}\}\) has a domain a:dom in the cube schema \(CS\) with a set of triples \(t_{\texttt{a}}\in T\) where \(t_{\texttt{a}}\) is represented as (a rdf:type qb:AttributeProperty; rdfs:domain xsd:Schema). Levels. A level \(l\in L=\{l_{1},l_{2},\ldots,l_{n}\}\) consists of a set of attributes \(A_{\texttt{l}}\), which is defined by a schema \(l(a_{1}\): dom\({}_{1}\),..., \(a_{n}\): dom\({}_{n})\), where l is the level, and each attribute a is defined over the domain dom. For each level \(l\in L\) in the cube schema CS, a set of triples \(tl\in T\), is represented as (l rdf:type qb4o:LevelProperty; qb4o:hasAttribute a). Relevant levels for FFB DW examples are the Plantation level and the Afdeling level, described in example 1. Adeling is an area in a plantation that is larger than a block. An afdeling has many blocks. Examples 1  
ffb:plantation rdf:type qb4o:LevelProperty;  
qb4o:hasAttribute ffb:plantationKey;  
qb4o:hasAttribute ffb:plantationName;  
qb4o:hasAttribute ffb:plantationGeo;  
qb4o:hasAttribute ffb:pMOGeo;  
qb4o:hasAttribute ffb:gateGeo. ffb:adeling rdf:type qb4o:LevelProperty;  
qb4o:hasAttribute ffb:adelingKey;  
qb4o:hasAttribute ffb:adelingName;  
qb4o:hasAttribute ffb:adelingGeo. Hierarchies. A hierarchy \(h\in H=\{h_{1},h_{2},\ldots,h_{n}\}\), in the cube schema \(CS\), is specified with a set of triples \(t_{\texttt{h}}\in T\), and represented as (h rdf:type qb4o:HierarchyProperty; qb4o:hasLevel l; qb4o:inDimension D).