=Paper=
{{Paper
|id=None
|storemode=property
|title=Non-Taxonomic Concept Addition to Ontologies
|pdfUrl=https://ceur-ws.org/Vol-969/paper6.pdf
|volume=Vol-969
}}
==Non-Taxonomic Concept Addition to Ontologies==
https://ceur-ws.org/Vol-969/paper6.pdf
Short Paper: Non-Taxonomic Concept Addition
to Ontologies
Artemis Parvizi, Chris Huyck, and Roman Belavkin
Middlesex University
The Borough
London NW4 4RL
Abstract. Concept addition, an ontology evolution’s edit operation,
includes adding taxonomic (hierarchical structure) and non-taxonomic
(concept properties) relations. Generating concept properties requires in-
formation extraction from various sources, such as WordNet. Other than
semantic similarities generated by WordNet, self-information generated
from existing non-taxonomic relations has aided non-taxonomic relation
addition to ontologies. Evaluation is based on using an ontology as gold
standard and detaching and reattaching the nodes. Non-taxonomic re-
lation generation without accessing an enormous amount of information
has proven to be quite difficult; the results displayed in this work are an
indication of this difficulty.
Keywords: Ontology Evolution, Ontology Learning, Non-Taxonomic
Relations, Concept Addition
1 Introduction
Ontology is commonly defined as a formal, explicit specification of a shared
conceptualisation [14], and often has been used for modelling concepts of the
world. Due to the experts’ limitations of producing a complete image of the
world with flexible boundaries for a domain, change is inevitable. Change in
ontologies has some common causes [29]: change in the domain, change in the
shared conceptualisation, or change in the specification. Ontology update has
been a subject of debate for many years, and many methods have been proposed
to address it. Ontology evolution and ontology learning are among these pro-
posed methods. Ontology evolution is “the timely adaptation of an ontology to
the arisen changes and the consistent propagation of these changes to dependent
artefacts” [39], such as systems defined in [5, 30, 22, 40, 13, 4, 42, 19, 21]; ontology
learning involves changing an ontology automatically or semi-automatically by
consulting some structured data sources, such as databases; semi-structured data
sources, such as WordNet, or Cyc; or some unstructured data sources, such as
text documents and web pages [10]. A few examples of ontology learning systems
can be found in [20, 9, 36, 27, 11, 41, 33].
Changing an ontology involves both changing the concepts and the relations.
Ontology relations have been divided into two categories: taxonomic relations
2 The Eighth Australasian Ontology Workshop
such as subClassOf and disjointWith in OWL [2], and non-taxonomic rela-
tions which covers most of the other OWL relations. On one hand, taxonomic
relations provide a structure to ontologies and are crucial. On the other hand,
non-taxonomic relations by presenting meaning add depth to the ontology. Re-
gardless of using the term ontology evolution or ontology learning, commonly,
ontology update involves changing both taxonomic and non-taxonomic relations.
A fundamental design operation for having a successful ontology evolution
application includes concept addition [24, 15]. To address concept addition, two
approaches (Approach I (see Section 4.1) and Approach II (see Section 4.2))
have been introduced in which ontology graphs (see Section 2) and semantic
similarity (see Section 3) have been employed.
2 Ontology Graph
The definition of an ontology in this paper is a set C of concepts and a set of
relations R1 , . . . , Rn , Ri ⊂ C × C. Since multiple relations with different labels
are allowed to exist in ontologies, labelled graphs also known as multigraphs
(G = (V, E1 , . . . , En )) with the set of vertices V ⇐⇒ C and a set of edges
Ei ⇐⇒ Ri are a logical choice of representing them. A graph with the stated
characteristics is called an ontology graph and is able to cover all important
structural OWL ontology features including individuals, classes, relations, ob-
ject properties, datatype properties, and restrictions [23]. The notion of ontology
graph in this work is an extended version represented in [26, 16, 34, 17, 3, 25];
vertices represent concepts, individuals, restrictions, and values, and edges, in-
clude taxonomic OWL relations, such as subClassOf and disjointWith, and
non-taxonomic relations.
3 Semantic Similarity
A successful ontology change application must be able to detect what needs
to be changed, gather sufficient information about the element that needs to
be changed, and finally decide how to implement change. Extracting relevant
and sufficient information is crucial. In this work, WordNet [38] and Wikipedia
as general purpose semi-structured data sources are consulted; they both are
capable of generating semantic similarity distances between concepts. Semantic
similarity between two or more concepts refers to the level of closeness that their
meanings possess, and it is very difficult to acquire. It is common practice to use
ontologies for computing the distance between two concepts and normalising the
final result. In RiTa WordNet [18], the minimum distance between any two senses
for the two words in the WordNet tree is returned and the result is normalised;
if there is a similarity a number is retuned, and 1 if no similarity is found.
This work has generated semantic similarities from Wikipedia as well. Al-
though many have mentioned that Wikipedia is much richer and a far better
source [35, 7, 32, 37], the result acquired from Wikipedia were not as promis-
ing as WordNet. Often semantic Wikipedia APIs only consult the infoboxes for
Non-Taxonomic Concept Addition to Ontologies 3
generating semantic similarity; lack of word sense when extracting concepts is
identified as another shortcoming [37].
4 Methodology
Ontology development is highly dependent on ontology experts, and domain
experts. The perception of an expert about a correct or an incorrect relation
may differ from another expert. This issue has contributed to the complexity of
ontology development and update. Nonetheless, this work proposes that when
adding a non-taxonomic relation, provided that the consistency of the ontol-
ogy holds and the ontological statement is semantically correct, the new state-
ment is as welcomed as any existing statement. For example when given the
three concepts Student, Library, and Group, and the relation memberOf, an
expert might generate Student memberOf some Library, Student memberOf
some Group, or both. Absence of either of these two statements will not make
the ontology incorrect but in certain circumstances it can be claimed that the
ontology is less accurate. The same justification holds when a system is auto-
matically generating non-taxonomic statements.
Commonly when generating non-taxonomic statements, a common approach
is to provide a set of possible properties for each concept, rank them accord-
ing to their frequencies, and finally according to some criteria select the highly
probably one. However, this work does not intend to generate new properties for
concept, but to assign an existing property to an input concept. Non-taxonomic
relations can be classified into two general groups: object properties (intrinsic
and extrinsic), and data-type properties [28]. The aim of this work is to gener-
ate intrinsic properties for a new input concept based on the existing intrinsic
properties. The hypothesis is that siblings of a vertex in an ontology graph often
have the same intrinsic properties assigned to different concepts.
In this work, the complete set of possible answers (Ans list) is generated,
and the existing statements in the ontology (Cur list) are extracted. Ans list is
a combination of an input concept I, the set of vertices V = V1 , V2 , . . . , Vn , the
set of edges E = E1 , E2 , . . . , En , and the set of restrictions. Note that in this
work only the two restrictions some and only are considered. Sample statements
for the following approaches are as follows:
Existing Statement: V1 E1 some V2
Generated Statement: I E1 some V3
4.1 Approach I
The members of list Ans for an input concept I, m vertices, the two restrictions,
and n edges will be 4 × m × n which comparative to list Cur are numerous.
This approach consists of a number of filters to prune Ans list according to Cur
list with the aid of various semantic similarities. To be able to apply semantic
similarities, a random entropy or self-information approach has been selected.
4 The Eighth Australasian Ontology Workshop
Probability of the event of randomly connecting a to b by an Ri relation is defined
by P (e) = P ((a, b) ∈ Ri ). The prior probability therefore being P (e) = k1 , where
k is the number of possible links (a, b) ∈ Ri . Given some semantic similarity
distances (see Section 3) s(a, b) ∈ [0, 1], the posterior probability of a connection
assuming a dependency between e and s(a, b) is:
P (e | s(a, b)) 6= P (e)
Since s(a, b) is a similarity distance (taking values in [0, 1] with 0 correspond-
ing to the most similar), it can be assumed that the posterior probability of
connection monotonically depends (∝) on 1 − s(a, b):
P (e | s(a, b)) ∝ 1 − s(a, b)
The monotonicity for two events e1 = (a, b) and e2 = (a, c) means the following:
s(a, b) ≥ s(a, c) ⇐⇒ 1 − s(a, b) ≤ 1 − s(a, c)
=⇒ P (e1 | s(a, b)) ≤ P (e2 | s(a, c))
The probability can be used to compute self-information as follows [6]:
h(a, b) = − log(P (e | s(a, b)))
≈ − log(1 − s(a, b))) (1)
The first filter is called hierarchy filtering; it is based on the patterns of the
siblings of the input concept. A sibling is referred to a concept with a disjoint-
With relation. This work focuses on non-taxonomic patterns. For the input con-
cept I, assuming that one of the statements in Ans is IE1 onlyV1 , the patterns
would be IE1 only and E1 onlyV1 . This approach only makes use of the forward
patterns which in this example is E1 onlyV1 . Any member of the Ans list which
does not contain the same pattern as one of the members of Cur list will be ex-
cluded from Ans. Also, if the input concept I and the first concept of a member
of Cur list do not have the same parent, the statement will be excluded from
Ans. Presuming both the pattern and the parent is matched, when the success
rate of comparing the generated statement with all the members of Cur list is
more than 50%, the statement will still remain in Ans, otherwise dropped. At
this stage, only the statements with the patterns similar to the existing non-
taxonomic statements remain.
From this point onwards, Equation 1 will aid the pruning process. For the
second filter Q1 = h(I, E1 ), Q2 = h(V3 , E1 ), Q3 = h(V2 , E1 ), and Q4 = h(V1 , E1 )
are generated. The goal of this filter is to investigate Q1 + Q2 ≤ Q3 + Q4 ∈ [0.1];
if in more than half the occurrences this function holds, then the generated
statement will be accepted; otherwise rejected. The aim is for the self-information
of the generated statement to be less than or equal to the self-information of the
current statements.
For the third filter Q5 = h(I, V1 ) and Q6 = h(V2 , V3 ) are calculated. This
filter will examine that in more than half the occurrences Q5 ≤ Q6 ∈ [0, 1] holds.
Non-Taxonomic Concept Addition to Ontologies 5
The forth filter will generate Q7 = h(I, V2 ) and Q8 = h(V1 , V3 ); the relation
Q7 ≤ Q8 ∈ [0, 1] must hold in more than half the occurrences for the generated
statement to be accepted.
The last filter will generate the self-information among all the members of
the generated and the current statement:
Qi = h(Statement f rom Ans list, Statement f rom Cur list)
The result generated by Qi are sorted and the k most similar statements
selected. Tables 1 and 2 display the results when k = 2.
4.2 Approach II
The members of the Ans list have to be pruned according to the members of Cur
list. A comparison between all the members of both lists is made. Providing that
a statement from one of lists has the same relation and restriction (for example
EK Some or EK Only) as the other list, the occurring pattern and its frequency
is recorded. The list containing the patterns P at will be sorted ascending with
regard to the frequencies, and the top half selected. Those statements in Ans
which do not contain these patterns will be omitted from the final answer pool.
The statement V1 E1 some V2 contains two patterns; (1) E1 some V2 and (2) V1
E1 some.
The aim of this step is to prune Ans list according to the patterns in Cur
list; there is a trade off to this filter, some semantically correct statements will
not be validated due to the low or lack of frequencies.
Hierarchy filtering as discussed in approach (I) will filter the remaining mem-
bers of the Ans list. When the siblings of the input concept contain a non-
taxonomic relation which have occurred in more than 50% of the cases and
this taxonomic relation is among the remaining members of the Ans list, this
statement will be accepted, otherwise rejected from Ans list.
4.3 Transitive Reduction
Both of the introduced approaches have the potential of producing transitive
relations, which from the consistency point of view have to be eliminated. Inher-
itance through the hierarchy has to be modelled in an ontology graph. Transitive
reduction on directed graphs is the answer to this problem. Presuming there is
the possibility of representing information in the directed graph G with fewer
arcs than the current amount, then that is the solution [1]. Graph G0 will be the
transitive reduction of G if it satisfies the following conditions:
1. A direct path between v and u in G0 exists, if a direct path between v and
u in G exists.
2. There is no graph with fewer arcs than G0 satisfying the above condition.
6 The Eighth Australasian Ontology Workshop
For approach (II), since all the remaining members of the Ans list are se-
lected, transitive reduction is applied after the last step. However, approach (I)
is more complicated due to selecting the top k generated relations. Transitive
reduction can be applied before or after the top k selection, which this work
has adopted the latter. Regardless of the approach, in situations in which a
child inherits a property and the algorithm identifies this transitive property,
the property is dropped.
4.4 Evaluation
This work has adopted an evaluation mechanism based on precision and recall
measurements [8, 12]. The strategy is to select a well-structured ontology and
after converting it into an ontology graph, detach the vertices one by one; the
system will attempt to reattach the vertex to the graph optimally with the
original relations and at the original location [31]. A comparison between the
number of removed edges in the original ontology graph (O) and the modified
graph (O0 ) is made. Assuming concepts c1 and c2 and relation Rk are present
in O0 , the hypothesis is to examine O and determine whether c1 and c2 are
related by Rk or not. Accepting the hypothesis indicates that O contains an
edge corresponding to c1 Rk c2 ; rejecting is when there is no such edge in O. The
overall count of correct edges in O0 relative to the numbers of all edges in O0
or O respectively will produce precision and recall. F-measure is a more just
measurement since precision and recall are distributed evenly.
|E ∩ E 0 | |E ∩ E 0 |
P (E 0 , E) = R(E 0 , E) =
|E 0 | |E|
P (E 0 , E)R(E 0 , E)
F (E 0 , E) = 2 ×
P (E 0 , E) + R(E 0 , E)
Other than studying the effect of a single concept addition, the effect of
adding a sequence of concepts also has to be studied. The order in which concepts
a and b are added to the system has an effect on the non-taxonomic relations
generated; generally, the semantic richness of the ontology is affected by the
existing concepts and relations. This work has studied the effect of adding two
(p = 2) and ten (p = 10) concepts to the ontology graph. Due to all the input
concepts being known, the average of all the possible orders have been displayed.
Approaches (I) clearly has better results than approaches (II) excluding one
exception. The more frequent a pattern, the higher the probability of it being
selected; also, the closer the pattern in the hierarchy, the greater the likelihood
of it being the final answer. The major difference between the two approaches
other than the F-measure is in the number of statements being selected as the
final answer. In the approach (I), the number of statements selected has a limit;
as a result, fewer unmatched statements are selected. However, approach (II)
has no limit on the number of generated statement, but at the same time more
unmatched statements are in the final answer pool. The reason this paper is
using the expression unmatched instead of incorrect is that studying the final
Non-Taxonomic Concept Addition to Ontologies 7
Table 1. The experimental results of non-taxonomic learning for approach (I). The
results are displayed in percentage.
p=1 p=2 p=10
Precision Recall F-measure Precision Recall F-measure Precision Recall F-measure
Pizza 0 0 unknown 0 0 unknown 0 0 unknown
Travel 25.0 50.0 33.33 25.0 50.0 33.33 25.0 50.0 33.33
Amino Acid 31.11 11.20 16.47 31.11 11.20 16.47 33.33 12.00 17.64
Career 20.00 26.66 22.85 20.00 26.66 22.85 15.00 20.00 17.14
Human and Pets 16.66 17.39 17.02 16.66 17.39 17.02 14.28 16.66 15.38
Movie 23.52 11.32 15.28 20.00 9.43 12.82 17.5 7.27 10.29
OBOE 0 0 unknown 0 0 unknown 0 0 unknown
University 19.56 14.51 16.66 19.56 14.51 16.66 11.36 8.06 9.43
Vehicle 14.28 18.18 16.0 14.28 18.18 16.0 23.07 27.27 25.0
Table 2. The experimental results of non-taxonomic learning for approach (II). The
results are displayed in percentage.
p=1 p=2 p=10
Precision Recall F-measure Precision Recall F-measure Precision Recall F-measure
Pizza 18.76 71.71 29.69 18.76 71.71 29.69 15.84 52.25 24.31
Travel 46.15 42.85 44.44 46.15 42.85 44.44 56.25 32.14 40.90
Amino Acid 52.50 63.00 57. 27 52.50 63.00 57. 27 59.42 41.0 48.52
Career 50 50 50 50 50 50 37.5 25.0 30.00
Human and Pets 52.77 39.58 45.23 52.77 39.58 45.23 57.57 39.58 46.91
Movie 45.16 70.0 54.90 48.83 70 57.53 49.33 61.66 54.81
OBOE 0 0 unknown 0 0 unknown 0 0 unknown
University 20.40 28.57 23.80 20.40 28.57 23.80 25.00 28. 57 26.66
Vehicle 0 0 unknown 0 0 unknown 0 0 unknown
results has shown that more than 50% of the unmatched statements are actually
semantically and logically accurate, although, not present in the original answer
pool. Nevertheless, Table (1) and 2 only display the result of correctly matched
edges to the original graph.
5 Conclusion and Future Work
One ontology evolution operation is concept addition, which implies adding a
concept by taxonomic and non-taxonomic relations. Commonly for changing an
ontology some external information is required. In this work WordNet as an ex-
ternal source for generating similarities between concepts and relations has been
8 The Eighth Australasian Ontology Workshop
selected. The semantic similarities generated by WordNet, self-information pro-
duced from patterns within ontologies, and the hierarchical structure of ontolo-
gies are the basis of approaches introduced in this paper. The focus is on intrinsic
properties; presuming that intrinsic properties already exist, the assumption is
that an input concept is more likely to have the same intrinsic properties as its
siblings. Evaluation is based on calculating the precision and recall of detaching
a node from an ontology and attempting to reattach it. The results displayed in
this paper are based on this evaluation technique. Due to the poor F-measures
generated by the introduced approaches, an investigation into the cause of this
poor performance revealed that more than 50% of the statements that were con-
sidered incorrect are actually semantically accurate. These results if generated
by an ontology expert, could easily be regarded as correct.
The next step for this research is to generate more complex non-taxonomic
relations, such as statements including conjunction and disjunction. Throughout
the development of this work, the need for a ternary and a quaternary comparison
has been visible. Such a comparison is essential for generating more meaningful
ontology statements. Another future direction is to develop a source capable of
ternary and quaternary comparison.
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