5.3 Ontology Matching
81
domain for which universal agreements are pursued from the ontological level to the
metaontological level, “the Tower of Babel becomes a Meta-Tower of Babel” [28].
As a consequence, semantic heterogeneity is seen as a necessary property of the
semantic web, and ontology matching and integration become basic features of its
successful mode of operation, rather than an expression of incompleteness. Options
for implementing such a mode of operation have been extensively discussed in the
literature, first for schemas and then for ontologies, cf. Noy [29] as well as Euzenat
and Shvaiko [30]. The common challenge is how to make use of the knowledge
represented in two ontologies, which can differ at various levels (language used,
expressivity, modelling paradigm, etc.). Typically, such challenges arise if there is
an overlap in the domains of knowledge addressed by multiple ontologies, such
that data annotated in diverse ways need to be combined and processed together, or
if a platform employs multiple domain ontologies that are based on different toplevel ontologies. Typical applications include, e.g. simultaneous querying of multiple
knowledge bases [31–34] or, as addressed here, the mapping of semantic content from
a source ontology S to a target ontology T .
Such a mapping α, by which a scenario A S expressed in the source ontology is
mapped to a A T expressed in the target ontology, is an ontology alignment. Equivalently, this can be applied to the corresponding knowledge graphs, α : G S → G T .
The process by which an alignment is constructed is known as ontology matching [35]. Alignments can be probabilistic or deterministic, e.g. in a probabilistic
formalism, it might be stated that “an osmo:condition that osmo:contains_variable an
evmpo:material_property has a 40% probability of being an emmo-models:Physics
BasedModel”, cf. Suchanek et al. [36]. For the present purpose, we restrict ourselves
to deterministic alignments, based on rules that are asserted to be valid in general. If
such an alignment is formulated coherently and correctly, the source and target scenarios need to be semantically consistent, i.e. the assertions from the target scenario
may not contradict the assertions from the source scenario, which can be checked in
multiple ways:
1. Immanently (ontologically), on the basis of a series of alignments α ◦ α
◦ . . . , at
the end of which another version of the scenario expressed in the source ontology is obtained. Then the consistency of the original and final scenarios can be
determined on the basis of the rules from the source ontology S.
2. Transcendentally (metaontologically), either by creating a new ontology that
encompasses both S and T , containing rules in which concepts or relations from
both ontologies occur jointly, or alternatively by a different system of—possibly
human—arbitration that can detect contradictions between A S and A T .
Under the constraint of consistency, it is the main challenge to preserve as much of
the originally given information as possible. Test scenarios, for which the desired
target representation is known, can be used to validate the alignment [34]. Moreover,
alignment rules, whether probabilistic or deterministic, can be obtained by evaluating
corpora of data that are annotated in both the source and target ontologies [35, 37];
in the probabilistic case, however, the outcome can be assumed to apply only as
long as the population or corpus underlying the statistical analysis from which the
81
domain for which universal agreements are pursued from the ontological level to the
metaontological level, “the Tower of Babel becomes a Meta-Tower of Babel” [28].
As a consequence, semantic heterogeneity is seen as a necessary property of the
semantic web, and ontology matching and integration become basic features of its
successful mode of operation, rather than an expression of incompleteness. Options
for implementing such a mode of operation have been extensively discussed in the
literature, first for schemas and then for ontologies, cf. Noy [29] as well as Euzenat
and Shvaiko [30]. The common challenge is how to make use of the knowledge
represented in two ontologies, which can differ at various levels (language used,
expressivity, modelling paradigm, etc.). Typically, such challenges arise if there is
an overlap in the domains of knowledge addressed by multiple ontologies, such
that data annotated in diverse ways need to be combined and processed together, or
if a platform employs multiple domain ontologies that are based on different toplevel ontologies. Typical applications include, e.g. simultaneous querying of multiple
knowledge bases [31–34] or, as addressed here, the mapping of semantic content from
a source ontology S to a target ontology T .
Such a mapping α, by which a scenario A S expressed in the source ontology is
mapped to a A T expressed in the target ontology, is an ontology alignment. Equivalently, this can be applied to the corresponding knowledge graphs, α : G S → G T .
The process by which an alignment is constructed is known as ontology matching [35]. Alignments can be probabilistic or deterministic, e.g. in a probabilistic
formalism, it might be stated that “an osmo:condition that osmo:contains_variable an
evmpo:material_property has a 40% probability of being an emmo-models:Physics
BasedModel”, cf. Suchanek et al. [36]. For the present purpose, we restrict ourselves
to deterministic alignments, based on rules that are asserted to be valid in general. If
such an alignment is formulated coherently and correctly, the source and target scenarios need to be semantically consistent, i.e. the assertions from the target scenario
may not contradict the assertions from the source scenario, which can be checked in
multiple ways:
1. Immanently (ontologically), on the basis of a series of alignments α ◦ α
◦ . . . , at
the end of which another version of the scenario expressed in the source ontology is obtained. Then the consistency of the original and final scenarios can be
determined on the basis of the rules from the source ontology S.
2. Transcendentally (metaontologically), either by creating a new ontology that
encompasses both S and T , containing rules in which concepts or relations from
both ontologies occur jointly, or alternatively by a different system of—possibly
human—arbitration that can detect contradictions between A S and A T .
Under the constraint of consistency, it is the main challenge to preserve as much of
the originally given information as possible. Test scenarios, for which the desired
target representation is known, can be used to validate the alignment [34]. Moreover,
alignment rules, whether probabilistic or deterministic, can be obtained by evaluating
corpora of data that are annotated in both the source and target ontologies [35, 37];
in the probabilistic case, however, the outcome can be assumed to apply only as
long as the population or corpus underlying the statistical analysis from which the