Semantic Mapping Concepts Based on Foundation Semantics

A standard set of semantic mapping concepts derive from foundation semantics (see Figure 6-6). This set of mapping concepts can be reused in all reconciliation scenarios since, following the SMIF approach, all domain

Satisfies certain conditions in “DomainX”

?x

Satisfies certain conditions in “DomainY”

?y

semanticMappingRelation

Tagged Remarks Tagged Remarks

models are essentially specialisations of the Foundation Layer, and therefore all share a common semantic ground.

Consider Figure 6-7 which illustrates how a semantic mapping concept can be specified for the reconciliation of cross-domain sub-classes of the foundation class “Round_Hole”. The expression accompanying the diagram captures the intuition that the “classMappingRelation_018” (A) be inferred as true between the arguments ?x and ?y if and only if ?x is a sub-class of “Round_Hole” defined within the “DomainX” context (B) and ?y is another sub-class of “Round_Hole” defined within the “DomainY” context (C).

(forall (?x ?y)

(<= (classMappingRelation_018 ?x ?y) (A)

(and (sup ?x Round_Hole)

(withinContext ?x DomainX) (B) (sup ?y Round_Hole) (withinContext ?y DomainY)))) (C) sup sup ?x Round_ Hole ?y classMappingRelation_018 DomainX DomainY

Figure 6-6 Semantic Mapping Concepts Based on Foundation Semantics

Figure 6-7 Example of a Class Semantic Mapping Concept Based on Foundation Semantics

Semantic Mapping Concepts

Domain Ontology Layer

Foundation Layer DomainX DomainY

Merged Domain Models

DomainX DomainY Semantic Reconciliation Layer

Although the name tag of the “classMappingRelation_018” carries very little information, yet, it is formally defined (refer to the logical expression in Figure 6-7). Informal remarks can be tagged to the semantic mapping relation, based on the formal logical conditions, to enhance the meaning of “classMappingRelation_018” between ?x and ?y for human interpretation. This can be achieved by stating, for example, that:

 There exists a commonality between the class ?x in the “DomainX” context and the class ?y in the “DomainY” context as a result of both ?x and ?y being subclasses of the foundation class “Round_Hole”. Both ?x and ?y capture the notion of a feature that is of cylindrical or conical negative (removal) volume. It is necessary for instances of ?x and ?y be defined in terms of a first instance of “Circular_Closed_Profile” swept along an instance of “Linear_Path” resulting in a second instance of “Circular_Closed_Profile” of identical or different dimensions. Every instance of ?x and ?y may be specified as holding a “Linear_Profile” axis.

The above informal statement is highly relevant in terms of interoperable semantics between the possible classes ?x and ?y, since the “Round_Hole” concept possesses formal necessary conditions, captured as integrity constraints, which restrict its interpretation (see also Chapter 5 section 5.2.2.4). Besides informal remarks about the semantic commonality, there is also the issue of dealing with uncertainties in ontology matching (Shvaiko and Euzenat, 2008) and in the case of the “classMappingRelation_018”, one way to specify this is to tag a limitation remark such as:

 Without reference to the terms assigned to the concepts ?x and ?y, there could potentially be class mismatches present. This is because ?x and ?y could have been defined with a view on specific domain preferences, which vary across domains. Varying levels of abstraction of the foundation class “Round_Hole” in both domains could also result in class mismatches.

The statement identified above is also relevant to semantic reconciliation in terms of the inconclusive correspondences that could exist between ?x and ?y. This is because the logical conditions for “classMappingRelation_018” do not entail term similarities nor the identification of the number of sub-class levels of “Round_Hole” in “DomainX” and “DomainY”. Hence, it is clear that possible semantic mismatches could still prevail even though the capability is present to infer similarities between ?x and ?y.

In a very similar way to the one explained, other semantic mapping concepts can be defined based on foundation semantics. Figure 6-8 depicts a scenario where a semantic mapping relation named “instanceMappingRelation_041”

(D) has been specified in order to partly reconcile domain-defined instances of

the class “Round_Hole”. The logical expression accompanying the figure states that the “instanceMappingRelation_041” (D) be inferred as true between the arguments ?holex and ?holey if and only if ?holex is an instance of “Round_Hole” defined within the “DomainX” context (E) and ?holey is another instance of “Round_Hole” defined within the “DomainY” context (F) and that both instances ?holex and ?holey share the common condition of having blind circular closed profiles (G).

The informal remarks which support the definition of the semantic mapping concept to partly reconcile round holes in “DomainX” and “DomainY” state that:

(forall (?holex ?holey ?ccpx ?ccpy)

(<= (instanceMappingRelation_041 ?holex ?holey) (D)

(and (inst ?holex Round_Hole)

(withinContext ?holex DomainX) (E)

(inst ?ccpx Circular_Closed_Profile) (holds_shape ?holex ?ccpx)

(blind ?ccpx) (G)

(inst ?holey Round_Hole)

(withinContext ?holey DomainY) (F)

(inst ?ccpy Circular_Closed_Profile) (holds_shape ?holey ?ccpy)

(blind ?ccpy)))) (G) inst inst ?holex Round_ Hole ?holey instanceMappingRelation_041 DomainX DomainY

Figure 6-8 Example of an Instance Semantic Mapping Concept Based on Foundation Semantics

 There exists a commonality between the instances ?holex and ?holey as a result of both being asserted instances of the foundation class “Round_Hole” declared in “DomainX” and “DomainY” respectively. ?holex and ?holey both share in common the property of having blind hole bottom conditions.

In this case the logical conditions that define “instanceMappingRelation_041” are very constrained and for this reason, no potential limitation could be envisaged over the semantic mapping concept. In other words, if the “instanceMappingRelation_041” holds true for two instance arguments ?holex and ?holey, then there is a total certainty that the semantic mapping concept applies under all circumstances (refer to Appendix E.1 for more information on other similar types of semantic mapping concepts that derive from foundation semantics).

6.2.2.2 Semantic Mapping Concepts Based on Known Cross-Domain