Ontology and Context by Hermann

 I. Cafezeiro, E. H. Haeusler and A. Rademaker, "Ontology and Context," 2008 Sixth Annual IEEE International Conference on Pervasive Computing and Communications (PerCom), Hong Kong, China, 2008, pp. 417-422, doi: 10.1109/PERCOM.2008.21.

1 Contextualized Entities

Entities are described by three parts: the entity itself, a context, and a link between the entity and its context. As both entity and context are ontologies, an entity can be the context of other entity. The context, gives general information about the entity or about the environment wherein the entity operates. Any context is linked to a (meta)context. The link between the entity and its context, plays the role of ensuring that the entity and its context are coherent, that is, the context respects (preserves) information concerning the nature of the entity.

[No KG o contexto também é parte do grafo, não é outro grafo que está linkado. Para as alegações o contexto são os qualificadores, pelo menos um subconjunto deles pq nem todo qualificador precisa ser mapeado em contexto e somente os contexto de interesse devem ser considerados. Outros contexto podem ser acrescentados depois.]

We divide the operations in three classes: Entity Integration, Context Integration and Combined Integration.

2 The Algebra of Contextualized Entities

2.1 Entity Integration

Operations in this class have the purpose of integrating entities that share the same context. As entities are coherent with respect to their context, an operation of this class is guided by the context and results a new entity that is also attached to that context .... By transitivity, the original context is also a context for the produced entity. ... This unique entity is the semantic intersection of E1 and E2 with respect to the context. Thus, if E1 and E2 give different approaches about a subject C, then E express their agreement with respect to C.

[E1 e E2 são integradas para gerar E. E1 e E2 estão ligadas a C, logo, E também estará ligada a C]

2.2 Context Integration

In Section 2.1 we showed an operation that results in an entity with more than one context. This situation happens not only as a consequence of that operation, but also in modeling many real world aspects, where a single entity can be viewed in different ways. This motivates the definition of a class of operations that act in the contexts of a single entity. A new context is produced as a result of combining and integrating given contexts. The resulting context must be coherent with respect to the corresponding entity.

[A entidade E está ligada aos conextos C1 e C2 (suponha que sejam duas fontes no contexto de proveniência). Os contextos são integrados para gerar o contexto C (suponha que seja uma classe fontes externas). A entidade E estará ligada a C também]

[Contexto Espaço-Temporal seria um novo contexto resultante da interseção (AND)]

2.3 Combined Integration

We defined ways of operating contextualized entities by combining entities (2.1) or contexts (2.2). In this section we show how to operate contextualized entities as a whole, considering both entity and context. We present the motivation for the operations and the formal definitions.

2.3.1 The Relative Intersection

The relative intersection gives commonalities among entities with different contexts. It is the coherent intersection of two given contextualized entities with respect to a third contextualized entity, and is performed in three contextualized entities, as in the diagram CE1 → CE ← CE2.

2.3.2 The Collapsing Union

The collapsing union of contextualized entities acts both in context and entity of contextualized entities and results the union of them, possibly collapsing some components. In a dual way of subsection 2.3.1, it is performed in three contextualized entities forming a diagram as CE1 ← CE → CE1.

3 The Formal Approach: Category Theory

Category Theory provides a great power of integration and interoperability of heterogeneous entities because of the focus that is put in relationship (categorical morphisms) and not in the “things” being represented (categorical objects). “Things” are described abstractly, accordingly to their interactions. It is possible to define several categories (according to the kinds of “things” to be described) that can be related by relationships between categories (categorical functors). Functors that preserve properties of categories making possible the co-existence of heterogeneous “things”. Category Theory offers a set of ways of combining entities, some of which (as colimits) are traditionally used to integration.

4 Conclusion

Considering that contexts are essential to clarify the meaning of entities, and that applications that consider dynamic changes of the environment require new forms of representing the context, we present in this paper an algebra to support the representation of contexts and to emphasize its relationships with entities. Abstraction, modularity and reuse are important properties that guide this approach, which are achieved by the uniform representation of entities and contexts and by the compositional definitions of operations. The role of an object (as entity or context) is given by the net of links from or to this object. Thus, the meaning of an entity is dependent of its relationships.

The notion of context is explicit and separated from the entity what ensures control over its context. Maintenance of context is transparent to the entity, that is free of knowing internal details of the context.

[Isolamento]

[Por exemplo o esquema do KG pode ser uma ontologia que possui partes como uma ontologia de domínio e outras partes como ontolgoias de fundamentação: PROV-O, GeoNames, Time Ontology, etc .... ]
[No CKG o mapeamento agrupa o tipo de contexto que a associação predicado X qualificador traz, acrescenta semântica]