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that inclusion relation simultaneously generalizes inheritance and can be used for type modeling like it
is done in object data models.
Both the relational model and COM are tuple-based and set-based. The main difference of COM is
that it introduces two types of tuples: identity tuples and entity tuples. Another difference is that instead
of using conventional sets, COM considered partially ordered sets. In other words, COM assumes that
in data modeling it is important to consider the structure of the set and partial order is assumed to be an
intrinsic and primary property of data while other properties are derived from it. One of the main achieve-
ments of the relational model was independence from physical representation which was reached by
removing physical (platform-specific) identities from the model. In this sense COM reverses the situation
by recognizing the importance of identity modeling. COM makes a clear statement that identities are at
least as important as entities and introduces special means for modeling them using concepts. If we as-
sume that surrogates are used for identifying rows in the relational model and then these surrogates may
have arbitrary structure then we get the mechanism of identity modeling similar to that used in COM.
The idea that partial order can be laid at the foundation of data management was also developed
by Raymond (1996) where “a partial order database is simply a partial order”. However, this approach
assumes that partial order underlies type hierarchies while COM proposes to use a separate inclusion
relation for modeling types. It also focuses on manipulating different partial orders and relies more on
formal logic while COM focuses on manipulating elements within one nested poset with strong focus
on dimensional modeling, constraint propagation and inference.
The notion of direct acyclic graph (DAG) has frequently been used in data modeling as a constraint
imposed on a graph structure. When used informally, DAGs and partial orders can be easily confused
although they are two different mathematical constructs created for different purposes. DAGs are more
appropriate for graph-based models to impose additional constraints on its relationships (edges of the
graph). COM is not a graph-based model and its main accent is made on dimensional modeling and
analytical functions where order theoretic formalism is much more appropriate. For example, in graphs
(including DAGs) we still rely on navigational approach for data access while in COM we rely on pro-
jection and de-projection operations along dimensions which change the level of details.
Hierarchies in the concept-oriented model are as important as they are in object data models (Dittrich,
1986, Bancilhon, 1996). However, object hierarchies are interpreted as inheritance and one of its main
purposes consists in re-use of parent data and behavior. COM inclusion relation generalizes inheritance
which means that inclusion can be used as inheritance. However, inclusion hierarchy is simultaneously
a means for identity modeling so that elements get their unique addresses within one hierarchical con-
tainer. Essentially, establishing the fact that inheritance is actually a particular case of inclusion is one
of the major contributions of the concept-oriented approach. From this point of view, hierarchy in the
hierarchical model and inheritance in object models are particular cases of inclusion hierarchy in COM.
The treatment of inclusion in COM is very similar to how inheritance is implemented in prototype-based
programming (Lieberman, 1986; Stein, 1987; Chambers et al, 1991) because in both approaches parent
elements are shared parts of children.
The use of partial order in COM makes it similar to multidimensional models (Pedersen et al, 2001)
widely used in OLAP and data warehousing. In most multidimensional models (Li et al, 1996; Agrawal
et al, 1997; Gyssens et al, 1997), each dimension type is defined as a partially ordered set of category
types (levels) and two special categories T (top) and L (bottom). The main difference is that COM pro-
poses to partially order the whole model without assigning special roles to dimensions, cube, fact table
and measures as it is done in multidimensional models. Thus instead of defining dimensions as several
