restrictions. However, built-ins are essential compo-
nents of SWRL necessary to implem ent mathematical
operations. The sepa ration of the representation into
different views can be considered a deficiency. A uni-
fied diagram for all three perspectives may improve
general understanding of the rule. Despite this, we
agree that the visual separation of rule antecedent and
consequent is as a good approach.
2.3 Graph Inscribed Logic (Grailog)
Grailog is a combination of g eneralised graph con-
structs fo r visualising data, inter alia, Horn logic
(Boley, 2013). The visualisation is adapted to the
industry standard RuleML. With Grailog a new
concept of hypergraphs is introduce d which is a
proposed enhancement in compar iso n to directed
labelled graphs (Boley, 2013). According to Boley,
directed labelled graphs (DLG) are a good starting
point for visual knowledge representation but come
with major disadvantages when trying to illustrate
non-binary relationships (Boley, 201 3). This is why
he created hyperarcs as specialised arrows for h is
notation. The following graphs show a c omparison
of a hypergraph on the left-hand side and a directed
labelled graph on the right-hand side (see Fig. 4).
Figure 4: Hypergraphs in comparison to DLG 1 (Boley,
2013).
Both diagrams in Fig . 4 show the two statements:
”John shows Latin to Kate”
”Mary teaches Latin to Paul”
Using a directed labelled gr a ph has the disadvantage
of losing th e context of input and output arrows
(Boley, 2013). This means that the graph may also
be misin te rpreted as “John shows Latin to Paul”
and “Mary teaches Latin to Kate”. However, the
hypera rcs provide a means to unmistakably define
the non -binary relationship. When trying to correctly
and unambiguously illustrate the two given sentences
as a DLG, the graph becom es significantly more
complex, demonstrating a major advantage of Grailog
Hypergraphs (see Fig. 5).
Grailog also offers the possibility to formulate advan-
ced logic using the idea of so called c omplex nodes.
According to Grailog, a graph can co nsist of elemen-
tary nodes such as John and Kate. Moreover, a com-
plex node is able to contain othe r grap hs, making it an
Figure 5: Hypergraphs in comparison to DLG 2 (Boley,
2013).
enclosing entity. Based on this, it is also possible to
express Horn Logic using a combination of complex
nodes in Grailog ( see Fig. 6) (Bo ley, 2013). Although
Grailog can describe Horn Logic, it is not specialised
for SWRL m aking it difficult to portray SWRL built-
ins. In this paper, we f ocus on a more specia lised
solution for SWRL ru le s.
Figure 6: Grailog - Horn logic (Boley, 2013).
2.4 Using UML State Diagrams for
Visualising Business Rules
In 2008, Konrad Kułakowski and Grzegorz J. Na-
lepa pu blished a modelling approach for business ru-
les using UML diagrams. The main idea is to repre-
sent a rule base as a class diagra m. Based on this,
each class repre sents a single rule. Th e class diagram
then shows dependenc ies between different rules (Ku-
lakowski and Nalepa, 200 8). Furtherm ore, each class
has its own state diagram which is describe d as a rule
definition d iagram. The paper defines rules a s plain
textual if-then statements (Kulakowski and N alepa,
2008). The rule d efinition diagram expresses condi-
tions using the UML standard Object Co nstraint Lan-
guage (OCL). As the proposed modelling format is
designed for business rules in g eneral, the possibili-
ties to visualise m ore complex SWRL logic rules are
limited.
3 CONCEPTUAL MODELLING
Before we define our notation elements we give a
brief discussion of relevant aspects of ontologies and
rules.