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MappedElement SequenceEdge ∃target.
(
ClosingGateway
∃
≤
2
incomingEdge.SequenceEdge
)
Required
(23)
target ◦ incomingEdge isRequired
(24)
Exclusive Branching.
Activities that appear in exclusive branches are sup-
posed to be exclusive, i.e., it is not allowed to execute activities from alternative
branches in a process execution. Axiom 25 defines each mapped element between
XOR-gateways as a subclass of
Exclude
.
MappedElement ∃successor.XORgateway ∃predecessor.XORgateway Exclude
(25)
Parallel Branching.
If activities occur in parallel branches, they have to be
executed commonly, i.e., if an activity of the first branch is executed, then also
the activity of the second branch is executed. In Axiom 26, we define elements
between AND-gateways as subclasses of the class
Conjunct
.
MappedElement ∃successor.AN Dgateway ∃predecessor.AN Dgateway Conjunct
(26)
4 Validation Using Description Logics
Our aim is to ensure that the well-formedness constraints are satisfied in all
process models that can be derived from a process model template. The con-
straints are represented by logical formulas, DL expressions in our case. We use
the expression
f
Φ
to represent a constraint on features and
f
Ω
to represent a
constraint on elements of the business process. From a logical point of view,
checking whether the constraint given by
f
Φ
ensures that the constraints repre-
sented by
f
Ω
hold, can be realized by checking whether the implication
f
Φ
⇒
f
Ω
holds for each interpretation, i.e.,
f
Φ
⇒
f
Ω
is a tautology.
f
Ω
for all mapped elements, we have
to tackle the following problems. (i) While the constraints in the problem space
are directly represented by the axioms, the constraints of the process model
template are implicitly given by the element's dependencies (cf. Sect. 3). Hence,
we have to
classify and derive
constraints of the mapped elements. (ii) We have
to guarantee that the same vocabulary and the same expression structure is used
in
f
Φ
and
f
Ω
. This is realized by
building constraint expressions
. (iii) Finally, we
have to check in DL whether the
implication
holds.
In Sect. 3.3, we specify implicit constraints of business processes and define
axioms in order to allow a dynamic classification of mapped and constrained
elements. These elements are categorized as subclasses of the classes
Required
,
Conjunct
and
Exclude
. Defined properties (
sibling
and
isRequired
)aswellastheir
inverse properties help to get their counterparts. E.g., for the conjunct element
E
, the counterpart (
E
) can be found by using the subsumption
E
In order to test the implication
f
Φ
⇒
sibling.E
.
∃
Building Constraint Expressions.
For the mapped elements, we build class
expressions
f
Φ
and
f
Ω
. To check the implication (subsumption in DL (
f
Φ
f
Ω
)),
