Databases Reference
In-Depth Information
To reason over contexts, we assume that the ontologies that these contexts
refer to are either included explicitly with
owl:imports
declarations or implicitly
by using property and class URIs that dereference directly to the data describing
the ontology itself. This later case should be the standard if the W3C best
practices for publishing ontologies [51] and the Linked Data principles [7] are
followed by data publishers. As ontologies might refer to other ontologies, the
import process then needs to be recursively iterated as explained in the next
section.
A naive approach would be to execute such a recursive fetching for each con-
textual graph and to create an
aggregate context
[28], i.e., the
RDF merge
of
the contextual graph and of the imported ontologies. At this point the deductive
closure of the aggregate context can be computed. Such a naive procedure is
however obviously inecient since a lot of processing time will be used to re-
calculate the T-Box deductions which could be instead reused for possibly large
numbers of other contextual graphs. Thus an ontology base is used to store and
reuse such deductions and is described next.
Reasoning with Contexts.
The notions of context and lifting rules presented
in the following are based on Guha's context mechanism [28]. Its aim is to control
the integration of data and ultimately avoid the aggregation of data that may
result in undesirable inferred assertions.
Within his framework, a
Context
is a first class resource and denotes the scope
of validity of a statement. The contents of the context are said to be true in that
context. This scope is defined by the symbol
ist
(“is true in context”), introduced
by Guha in [27]. The notation
ist
(
c, ϕ
) states that a proposition
ϕ
is true in the
context
c
. Since contexts are first class objects, it becomes possible to define
expressive formulae whose domains and ranges are contexts. An example is the
so called
Lifting Rule
that enables to
lift
axioms from one context to another.
An
Aggregate Context
is a subclass of
Context
. Its content is composed by the
contents lifted from other contexts. An aggregate context must contain the full
specification of what it imports. In our case, each contextual graph is considered
an
Aggregate Context
, since it always contains the specification of what it imports
through explicit or implicit import declarations, as explained next.
Import Closure of RDF Models.
On the Semantic Web, ontologies are
published in order to be easily reused by third parties. OWL provides the
owl:imports
primitive to indicate the inclusion of a target ontology inside an
RDF model. Conceptually, importing an ontology brings the content of that
ontology into the RDF model.
The
owl:imports
primitive is transitive. That is, an import declaration states
that, when reasoning with an ontology
O
, one should consider not only the
axioms of
O
, but the entire
import closure
of
O
.The
import closure
of an ontology
O
is the smallest set containing the axioms of
O
and all of the axioms from the
ontologies that
O
(transitively) imports. For example, if ontology
O
A
imports
O
B
,and
O
B
imports
O
C
,then
O
A
imports both
O
B
and
O
C
.
