Abstract
The concept-oriented model (CoM) is a new approach to data modeling (Savinov, 2004) that is being developed along with concept-oriented programming (CoP) (Savinov, 2005a). Its major goal consists of providing simple and effective means for representing and manipulating multidimensional and hierarchical data while retaining the possibility to model how the data are represented physically. Thus, this model has two sides or flavors: logical and physical. From the point of view of logical structure, CoM belongs to a class of multidimensional models (Agrawal, Gupta, & Sarawagi, 1997; Gyssens & Lakshmanan, 1997; Li & Wang, 1996) and OLAP technologies (Berson & Smith, 1997). The main difference from the existing approaches is that CoM is based on the theory of ordered sets. Particularly, one source of inspiration when developing CoM was formal concept analysis (FCA) and lattice theory (Ganter & Wille, 1999).
TopIntroduction
Background
The concept-oriented model (CoM) is a new approach to data modeling (Savinov, 2004) that is being developed along with concept-oriented programming (CoP) (Savinov, 2005a). Its major goal consists of providing simple and effective means for representing and manipulating multidimensional and hierarchical data while retaining the possibility to model how the data are represented physically. Thus, this model has two sides or flavors: logical and physical. From the point of view of logical structure, CoM belongs to a class of multidimensional models (Agrawal, Gupta, & Sarawagi, 1997; Gyssens & Lakshmanan, 1997; Li & Wang, 1996) and OLAP technologies (Berson & Smith, 1997). The main difference from the existing approaches is that CoM is based on the theory of ordered sets. Particularly, one source of inspiration when developing CoM was formal concept analysis (FCA) and lattice theory (Ganter & Wille, 1999).
Elements in the concept-oriented model are living among other elements within a multidimensional hierarchical structure (Savinov, 2005b). This means that any element has a number of parents and children. The direct and indirect neighbors determine its semantic properties while the element itself is thought of as an identifier. So the meaning of an element is distributed all over the model within the ordered structure and depends on its relative position among other elements. One important property of CoM that is absent in most other models is that it possesses canonical semantics. It makes many problem formulations and solutions much simpler because operations can be applied directly to the semantics of the whole model represented using primitive dimensions rather than to different local elements. In particular, it is very important for such a mechanism as grouping and aggregation (Savinov, 2006a), and constraint propagation and inference (Savinov, 2006b). In this sense, CoM is analogous to the universal relation model (URM) where all relations are assumed to be projections of a single relation (Fagin, Mendelzon, & Ullman, 1982; Kent, 1981; Maier, Ullman, & Vardi, 1984).
The multidimensional and hierarchical structure underlying the concept-oriented model can be used for navigational purposes (Savinov, 2005c). This means that data can be accessed by specifying a logical path rather than using joins. In this sense, CoM is similar to the functional data model (FDM; Gray, Kerschberg, King, & Poulovassilis, 2004; Gray, King, & Kerschberg, 1999; Shipman, 1981). The difference is that the mechanism of logical navigation in CoM relies on the ordered structure of elements rather than using an arbitrary graph.
Key Terms in this Chapter
Inverse Dimension: A dimension with the opposite direction. Inverse dimension can be viewed as a downward path in the concept graph. Inverse dimensions are interpreted as multivalued attributes.
Dimension: A named link between this concept and some of its direct superconcepts. It is analogous to a column. The superconcept in this case is referred to as a domain of this dimension.
Dimension of Rank k: A sequence of dimensions leading from this concept to some of its superconcepts where each next dimension belongs to the domain of the previous dimension. Dimension of rank k can be viewed as an upward path in the concept graph. Dimensions are interpreted as single-valued attributes.
Access Path: A sequence of projection and deprojection operations applied to the source subset of items. Access paths are used for the logical navigation and retrieval of related items and can include additional constraints.
Deprojection: An operation applied to a set of items that returns a subset of their subitems referencing the source items along the specified dimension. Multidimensional deprojection uses several bounding dimensions leading from the selected subconcept to the superconcept.
Concept: A data modeling construct that physically includes a number of data items and logically has a number of parent concepts and child concepts. Parent concepts are referred to as superconcepts while child concepts are referred to as subconcepts.
Projection: An operation applied to a set of items that returns a subset of their superitems referenced by the source items along the specified dimension. Multidimensional projection uses many bounding dimensions leading from the source concept to the selected superconcept.
Primitive Concept: A direct subconcept of a top concept.
Top Concept: A direct or indirect superconcept for any other concept in the model. It is the most general concept that is introduced formally.
Bottom Concept: A direct or indirect subconcept for any other concept in the model. It is the most specific concept in the model that can be introduced formally if it does not exist.