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the node. Therefore, the concept of the node
HotelInfo.city
is the conjunction of the
concept
HotelInfo
and the concept
city
.
The third step involves the creation of a semantic relationship matrix for each
pair of atomic concepts, based on node information only. This can be done either
by using common string matching techniques or by using a thesaurus such as Word-
net. For the latter, equivalence is determined if there is at least one sense that is
defined as a synonym. Subsumption is determined if a sense in one concept is a
hypernym or holonym of a sense in the other concept. Disjointness is defined if two
senses of the two concepts are different hyponyms of the same synonym set or if
they are antonyms. For example, assume the use of string matching and Wordnet.
HotelInfo
and
HotelCardInformation
will be (mistakenly) considered to be equiv-
alent, both because of the identical
Hotel
label and because
Info
and
Information
are synonyms.
The fourth step takes all pairs of nodes and computes a semantic relationship
matrix based on the positioning of nodes within their own ontologies. Semantic
relations are translated into propositional connectives, with equivalence being trans-
lated into equivalence, subsumption into implication, and disjointness into negation.
Then, the following formula is checked for satisfiability:
!
C
rel.C
i
;C
j
/:
C
i
and C
j
are the concepts of nodes i and j in the two schemas, as generated in the
first step and C is the conjunction of all the relations that hold between concepts of
labels mentioned in C
i
and C
j
(this includes all nodes on the path to nodes i and j ).
This is done by using a SAT solver to test unsatisfiability. It is worth noting that
the unsatisfiability problem is known to be CO-NP, yet modern SAT solvers have
shown very good performance in solving such problems. To reason about relations
between concepts of nodes, a set of premises (axioms) is built as a conjunction of the
concepts of labels computed in the third step. For example,
R.CardInfo.type
will
be defined to be subsumed by
S.CardInformation
while an equivalence semantic
relationship is defined between
R.CardInfo.type
and
S.CardInformation.type
.
4.2
Discussion
A few other methods for finding semantic attribute correspondences were suggested
in the literature. For example, Chimaera [
McGuinness et al. 2000
] finds equiva-
lences, subsumptions, and disjointness among attributes (ontology terms in this
case). As another example, FCA-Merge [
Stumme and Maedche 2001
] identifies
subsumptions using a natural language document corpus.
Semantic attribute correspondences can be modeled using the similarity matrix
model (see Sect.
2
). Each ontological relationship is modeled as a separate matrix
(one matrix for equivalence, one for subsumption, etc.). These matrices represent
the confidence level in an ontological relationships, as generated in the first two
