Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
Teeradaj Racharak
1,2
and Satoshi Tojo
2
1
School of Information, Computer, and Communication Technology, Sirindhorn International Institute of Technology,
Thammasat University, Pathum Thani, Thailand
2
School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan
Keywords:
Concept Similarity Measure, Semantic Web Ontology, Preference Profile, Description Logics.
Abstract:
In Description Logics (DLs), concept similarity measure aims at identifying a degree of commonality of two
given concepts and is often regarded as a generalization of the classical reasoning problem of equivalence.
That is, any two concepts are equivalent if and only if their similarity degree is one. When two concepts are
not equivalent, the level of similarity varies depending not only on the objective factors (e.g. the structure
of concept descriptions) but also on the subjective factors (i.e. the agent’s preferences). Realistic ontologies
are generally complex. Methodologies for tuning a measure to conform with the agent’s preferences should
be practical, i.e. it is doable in practice. In this work, we investigate and formalize the task of tuning the
preference functions based on the information defined in a TBox and an ABox. We also show how the proposed
approaches can be reconciled with the measure sim
π
, i.e. a concept similarity measure under preference profile
for DL ELH . Finally, the paper relates the approach to others and discusses future direction.
1 INTRODUCTION
Most Description Logics (DLs) are decidable frag-
ments of first-order logic (FOL) (Baader et al., 2010)
with clearly defined computational properties. DLs
are the logical underpinnings of the DL flavor of
OWL and OWL 2. The advantage of this close con-
nection is that the extensive DLs literature and im-
plementation experiences can be directly exploited by
OWL tools. More specifically, DLs provide unam-
biguous semantics to the modeling constructs avail-
able in the DL flavor of OWL and OWL 2. These
semantics make it possible to formalize and design
algorithms for a number of reasoning services, which
enable the development of ontology applications to
become prominent. For instance, ontology classifi-
cation (or ontology alignment) organizes concepts in
an ontology into a subsumption hierarchy and assists
in detecting potential errors of a modeling ontology.
Though this subsumption hierarchy inevitably bene-
fits ontology modeling, it merely gives two-valued
responses, i.e. inferring a concept is subsumed by
another concept or not. However, certain pairs of
concepts may share commonality even though they
are not subsumed. As a consequence, a considerable
amount of research effort has been devoted on mea-
suring similarity of two given concepts, i.e. a problem
of concept similarity measure in DLs.
Basically, a concept similarity measure (CSM) is
a function mapping from a concept pair to a unit in-
terval (i.e. 0 x 1 for any real number x). The
higher the value is mapped to, the more likely sim-
ilarity of them may hold. Intuitively, the value 0
can be interpreted as total dissimilarity whereas the
value 1 can be interpreted as total similarity or equiv-
alence. Hence, one may regard concept similarity
measure as a generalization of the classical reason-
ing problem of equivalence. Its idealistic objective
is to imitate similarity identification performed by a
human expert. It plays a major role in the discovery
of similar concepts in an ontology. For example, it is
employed in bio-medical ontology-based applications
to discover functional similarities of gene (Ashburner
et al., 2000), it is often used by ontology alignment
algorithms (Euzenat and Valtchev, 2004). There is
currently a significant number of measures in DLs.
Prominent examples are (Janowicz and Wilkes, 2009;
Racharak and Suntisrivaraporn, 2015; D’Amato et al.,
2006; Fanizzi and D’Amato, 2006; D’Amato et al.,
2009; D’Amato et al., 2008; Racharak et al., 2016b).
However, these measures are devised based on objec-
tive factors (a notable exception is (Racharak et al.,
2016b) where a concept similarity measure under an
agent’s preferences is discussed.). For example, they
use the structure (or interpretations) of concept de-
scriptions in question to measure. When these mea-
Racharak T. and Tojo S.
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH.
DOI: 10.5220/0006249602870298
In Proceedings of the 9th International Conference on Agents and Artificial Intelligence (ICAART 2017), pages 287-298
ISBN: 978-989-758-220-2
Copyright
c
2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
287
sures are employed to characterize similar concepts
in an ontology, they may lead to unintuitive results.
It may even be contradictory to an intuitive under-
standing of an application domain. The following ex-
ample illustrates that using objective-based measures
may not suffice to answer an agent’s request.
Example 1.1 An agent A wants to visit a place for do-
ing some active activities. At that moment, he would
like to enjoy walking. Suppose that a place ontology
has been modeled as follows:
ActivePlace v Place u canWalk.Trekking
u∃canSail.Kayaking
Mangrove v Place u canWalk.Trekking
Beach v Place u canSail.Kayaking
canWalk v canMoveWithLegs
canSail v canTravelWithSails
Suppose that a measure used by that Agent A
considers merely the objective aspects, it is reason-
able to conclude that both Mangrove and Beach are
equally similar to the concept ActivePlace. However,
by taking into account also the agent’s preferences,
Mangrove appears more suitable to his perception of
ActivePlace at that moment. In other words, he will
not be happy if an intelligent system happens to rec-
ommend him to go for a Beach.
The example shows that preferences of an agent
play a decisive role in the choice of alternatives. In
essence, when the choices of an answer are not to-
tally similar to a concept in question, a measure may
need to be tuned by subjective factors, e.g. an agent’s
preferences. A set of preferential aspects is identi-
fied in (Racharak et al., 2016a) called preference pro-
file and is extended toward (Racharak et al., 2016b)
called sim
π
. However, realistic ontologies are com-
plex – consisting in plenty of concept names and role
names. Tuning a measure to conform with the agent’s
preferences should be practical, i.e. it is doable in
practice. Hence, our primary motivation of this work
is a deeper understanding of how preference profile is
configured. In this work, we investigate and formal-
ize the task of configuring the preference functions
based on the information defined in a TBox and an
ABox (cf. Section 3). This work is an extension of
(Racharak et al., 2016b): with respect to its prede-
cessor, it shows how the proposed approaches can be
reconciled with the measure sim
π
, i.e. a concept simi-
larity measure under preference profile for DL E LH
(cf. Section 4). Preliminaries is briefly reviewed in
Section 2. Finally, the paper relates the approach to
others (cf. Section 5 and Section 6) and discusses fu-
ture direction (cf. Section 7).
2 PRELIMINARIES
In this section, we review the basics of Description
Logic ELH (cf. Subsection 2.1), which provides the
logical underpinning for OWL 2 EL (Group, 2012;
Grau et al., 2008) and our developed measure sim
π
(originally introduced in (Racharak et al., 2016b)) is
based. After that, we briefly explain the notion of
preference profile in Subsection 2.2.
2.1 Description Logic ELH
We assume countably infinite sets CN of concept
names, RN of role names, and IN of individual names
that are fixed and disjoint. The set of concept descrip-
tions, or simply concepts, for a specific DL L is de-
noted by Con(L). The set Con(ELH ) of all ELH
concepts can be inductively defined by the following
grammar:
Con(ELH ) ::= A | > | C u D | r.C
where > denotes the top concept, A CN, r RN,
and C, D Con(E LH ). Conventionally, concept
names are denoted by A and B, concept descriptions
are denoted by C and D, and role names are denoted
by r and s, all possibly with subscripts.
A terminology or TBox T is a finite set of (possi-
bly primitive) concept definitions and role hierarchy
axioms, whose syntax is an expression of the form
(A v D) A D, and r v s, respectively. A TBox is
called unfoldable if it contains at most one concept
definition for each concept name in CN and does not
contain cyclic dependencies. Concept names occur-
ring on the left-hand side of a concept definition are
called defined concept names (denoted by CN
def
), all
other concept names are primitive concept names (de-
noted by CN
pri
). A primitive definition A v D can
easily be transformed into a semantically equivalent
full definitions A X u D where X is a fresh con-
cept name. When a TBox T is unfoldable, concept
names can be expanded by exhaustively replacing all
defined concept names by their definitions until only
primitive concept names remain. Such concept names
are called fully expanded concept names. Like prim-
itive definitions, a role hierarchy axiom r v s can be
transformed in to a semantically equivalent role def-
inition r t u s where t is a fresh role name. Role
names occurring on the left-hand side of a role defini-
tion are called defined role names, denoted by RN
def
.
All others are primitive role names, collectively de-
noted by RN
pri
. We also denote a set of all rs super
roles by R
r
= {s RN|r = s or r
i
v r
i+1
T where
1 i n, r
1
= r, r
n
= s}.
An assertion or ABox A is a finite set of concept
assertions and role assertions whose syntax is an ex-
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
288
pression of the form C(a) and r(a, b) where a, b IN,
respectively. An ontology O consists of a TBox T
and an ABox A, i.e. O = hT , Ai. However, some
existing ontologies may omit an ABox A in practice.
An interpretation I is a pair I = h
I
, ·
I
i where
I
,
is a non-empty set representing the domain of the in-
terpretation and ·
I
is an interpretation function which
assigns to every concept name A a set A
I
I
, and
to every role name r a binary relation r
I
I
×
I
.
The interpretation function ·
I
is inductively extended
to ELH concepts in the usual manner:
>
I
= ; (C u D)
I
= C
I
D
I
;
(r.C)
I
= {a
I
| b
I
: (a, b) r
I
b C
I
}.
An interpretation I is said to be a model of a TBox T
(in symbols, I |= T ) if it satisfies all axioms in T . I
satisfies axioms A v C, A C, and r v s, respectively,
if A
I
C
I
, A
I
= C
I
, and r
I
s
I
. Also, an interpre-
tation I is said to be a model of an ABox A (in sym-
bols, I |= A) if it satisfies all axioms in A. I satisfies
axioms C(a) and r(a, b) if a
I
C
I
and (a,b) r
I
, re-
spectively. Furthermore, an interpretation I is said to
be a model of an ontology O if it satisfies all axioms in
T and A. An interpretation I
A
is called the canonical
interpretation if:
1.
I
A
of I
A
consists of all individual names in A;
2. A CN, we define A
I
A
= {x | A(x) A}; and
3. r RN, we define r
I
A
= {(x, y) | r(x, y) A}.
That is, the canonical interpretation I
A
is the interpre-
tation which takes the set of ABox as the interpreta-
tion domain.
The main inference problem for ELH is the sub-
sumption problem. That is, given C, D Con(ELH )
and an ontology O, C is subsumed by D w.r.t. O (in
symbols, C v
O
D) if C
I
D
I
for every model I of
O. Furthermore, C and D are equivalent w.r.t. O (in
symbols, C
O
D) if C v
O
D and D v
O
C. A much
more interesting inference problem, which is based on
concept subsumption, is the concept hierarchy. That
is, let CN(O) be the concept names occurring in O,
the concept hierarchy of O is the most compact repre-
sentation of the partial ordering (CN(O), v
O
) induced
by the subsumption relation w.r.t O. When an ontol-
ogy O is empty or is clear from the context, we omit
to denote O, i.e. C v D or C D. Furthermore, a
more generalization of the concept equivalence is a
concept similarity measure under preference profile
(cf. Definition 2.3), which is originally introduced in
(Racharak et al., 2016b).
2.2 Preference Profile
We first introduced preference profile (denoted by π)
in (Racharak et al., 2016a) as a collection of pref-
erential elements in which the development of con-
cept similarity measure should consider. Its first intu-
ition is to model different forms of preferences (of an
agent) based on concept names and role names. Mea-
sures adopted this notion are flexible to be tuned by an
agent and can determine the similarity conformable to
that agent’s perception. We give a formal definition of
each preferential aspect in the following definition.
Definition 2.1 (Preference Profile (Racharak et al.,
2016a)). Let CN
pri
(T ), RN
pri
(T ), and RN(T ) be a
set of primitive concept names occurring in T , a set
of primitive role names occurring in T , and a set of
role names occurring in T , respectively. A preference
profile, in symbol π, is a quintuple hi
c
, i
r
, s
c
, s
r
, di
1
where
i
c
: CN [0, 2] where CN CN
pri
(T ) is called
primitive concept importance;
i
r
: RN [0, 2] where RN RN(T ) is called role
importance;
s
c
: CN × CN [0, 1] where CN CN
pri
(T ) is
called primitive concepts similarity;
s
r
: RN × RN [0, 1] where RN RN
pri
(T ) is
called primitive roles similarity; and
d : RN [0, 1] where RN RN(T ) is called role
discount factor.
We discuss the interpretation of each above func-
tion in order. Firstly, for any A CN
pri
(T ), i
c
(A) = 1
captures an expression of normal importance on A,
i
c
(A) > 1 (i
c
(A) < 1) indicates that A has higher (and
lower, respectively) importance, and i
c
(A) = 0 indi-
cates that A has no importance to the agent. Sec-
ondly, we define the interpretation of i
r
in the simi-
lar fashion as i
c
for any r RN(T ). Thirdly, for any
a, b CN
pri
(T ), s
c
(A, B) = 1 captures an expression
of total similarity between A and B and s
c
(A, B) = 0
captures an expression of total dissimilarity between
A and B. Fourthly, the interpretation of s
r
is defined
in the similar fashion as s
c
for any r, s RN
pri
(T ).
Lastly, for any r RN(T ), d(r) = 1 captures an ex-
pression of total importance on a role (over a corre-
sponding nested concept) and d(r) = 0 captures an ex-
pression of total importance on a nested concept (over
a corresponding role).
Definition 2.2 (Default Preference Profile
(Racharak et al., 2016a)). The default preference
profile, in symbol π
0
, is the quintuple hi
c
0
, i
r
0
, s
c
0
, s
r
0
, d
0
i
1
In the original definition of preference profile
(Racharak et al., 2016a; Racharak et al., 2016b), both i
c
and i
r
are mapped to R
0
, which is a minor error.
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
289
where
i
c
0
(A) = 1 for all A CN
pri
(T ),
i
r
0
(r) = 1 for all r RN(T ),
s
c
0
(A, B) = 0 for all (A, B) CN
pri
(T ) × CN
pri
(T ),
s
r
0
(r, s) = 0 for all (r, s) RN
pri
(T ) × RN
pri
(T ),
d
0
(r) = 0.4 for all r RN(T ).
Let us also note that the value of d
0
determines
how important the existential information should be
considered by a measure in the default manner (see
the interpretation of d). This information is indeed
dependent on an application domain and might be re-
defined. For instance, if d
0
is defined as 0.3, 0.4, 0.5,
then part.Heart
π
T
part.Colon yields 0.3, 0.4, 0.5,
respectively.
2
In the following, we give the formal
definition of concept similarity measure under prefer-
ence profile.
Definition 2.3 ((Racharak et al., 2016b)). Given a
preference profile π, two concepts C, D Con(L),
and a TBox T , a concept similarity measure un-
der preference profile w.r.t. a TBox T is a func-
tion
π
T
: Con(L) × Con(L) [0, 1]. A function
π
T
is called preference invariance w.r.t equivalence
if C D (C
π
T
D = 1 for any π).
Taking π = π
0
for a concept similarity measure
under preference profile, i.e.
π
0
T
, obtains an objective
similarity degree. We prove this in Theorem 3.1 of
(Racharak et al., 2016b).
3 STRATEGIES OF TUNING π
3.1 Tuning i
c
This subsection exhibits a strategy for tuning primi-
tive concept importance i
c
in practice. Realistic on-
tologies are generally complex consisting in plenty
of concept names. Hence, having some strategies of
tuning is useful since it helps to pave the way for a
more convenient use of preference profile.
As a starting point, we seek to observe characteris-
tics of realistic ontologies whose TBox is unfoldable
3
,
e.g. a popular medical ontology SNOMED, denoted by
O
med
, (Stearns et al., 2001). Figure 1 gives an exam-
ple of concept definitions in O
med
and Figure 2 shows
the concept hierarchy w.r.t. O
med
.
2
These numbers is obtained from an application of sim
π
. Its
precise definition is given in Section 4.
3
According to this investigation, we assume an ontology
O has an unfoldable TBox T in this work.
Pericardium v Tissue u part.Heart
Endocardium v Tissue u part.Heart
Appendicitis Inflammation
u∃loc.Appendix
Pericarditis Inflammation
u∃loc.Pericardium
Endocarditis Inflammation
u∃loc.Endocardium
Inflammation v Disease
HeartDisease Disease u loc.part.Heart
Figure 1: Example of concept definitions in O
med
.
>
Tissue
Endocardium
Pericardium
Heart
Disease
HeartDisease
Endocarditis
Pericarditis
Inflammation
Appendicitis
Figure 2: The concept hierarchy of O
med
.
According to the above figures, it is intuitive to ex-
press primitive concept importance through the con-
cept hierarchy. For instance, an agent may say my
concept importance goes through Disease; or my
concept importance goes through HeartDisease. In-
formally investigating, let CN
pri
(O
med
) be a set of
primitive concept names occurring in O
med
. Since
Disease CN
pri
(O
med
), the former case is simple,
e.g. an agent may mean i
c
(Disease) = 1.2. The lat-
ter case is a bit complicated since HeartDisease 6∈
CN
pri
(O
med
). However, the agent’s intention may
mean i
c
(Disease) = 1.2 and i
c
(Heart) = 1.2. This
informal investigation shapes the development as fol-
lows:
Definition 3.1. Let CN(T ) (CN
pri
(T ) and CN
def
(T ))
be a set of concept names (primitive concept names
and defined concept names, respectively) occurring
in T . Then, a propagation for primitive concept im-
portance is a partial function I
c
: CN
0
[0, 2], where
CN
0
CN(T ) {>}, such that a mapping n of I
c
on
X (i.e. I
c
(X) = n) is defined inductively as follows:
4
.
1. X CN
pri
(T ) i
c
(X) = n;
2. X
:
= > x CN
pri
(T ) : i
c
(x) = n; and
3. X CN
def
(T ) x RHS(X) : I
c
(x) = n.
where RHS(X ) is a set of concept names appearing
on the right-hand side of X.
Its interpretation is defined in a usual way. That is,
for any A CN(T ), I
c
(A) = 1 captures an expression
of normal importance on A, I
c
(A) > 1 (and I
c
(A) <
4
Later, we discuss some restrictions the readers should
take into account when the notion I
c
is employed.
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
290
1) indicates that A has higher (and lower, respectively)
importance, I
c
(A) = 0 indicates that A has no impor-
tance to the agent. For the special case, I
c
(>) = n
indicates that every primitive concept name occurring
on T is of equal importance at n.
Example 3.1. From Figure 1, suppose that an agent
A is using a concept similarity measure under pref-
erence profile for querying some names that expose
the similar characteristics to HeartDisease. Thus, the
agent can express a preference I
c
(HeartDisease) =
1.2 instead of individually specifying i
c
(Disease) =
1.2 and i
c
(Heart) = 1.2.
There are a few concerns that we should take into
account, i.e. (1) inconsistent preferences of concepts
occurring on the same branch of the concept hierar-
chy; (2) inconsistent preferences of defined concepts
occurring on different branches of the concept hierar-
chy; and (3) expressing preferences when a TBox T
contains equivalent defined concepts.
Let us take a look on our first concern through the
following preference expression: my concept impor-
tance goes through Disease, especially HeartDisease.
In this example, we may take I
c
(Disease) = 1.2 and
I
c
(HeartDisease) = 1.3. Here, Disease is redefined
on i
c
twice. This kind of scenarios is possible to
happen because we are extending the aspect of primi-
tive concept importance toward both types of concept
names. There are many ways to handle this with the
use of operators : [0, 2]
2
[0, 2].
Definition 3.2. Let A CN
pri
(T ) be a set of primi-
tive concept names occurring in T and x
0
, x
1
[0, 2].
Also, let i
c
(A) = x
0
be the previous mapping on A.
We compute a new mapping i
c
(A) = x
1
as follows:
i
c
(A) =
(
x
1
if i
c
is not defined on A
x
0
x
1
otherwise
(1)
The notion of the operator remains abstract here as
its concrete operators may vary on the context of use.
In the following, we establish some of the abstract
notion , i.e.
max
,
first
, and
last
. Let two real
numbers x
1
, x
0
[0, 2]. Then,
x
0
max
x
1
= max{x
0
, x
1
} (2)
x
0
first
x
1
= x
0
(3)
x
0
last
x
1
= x
1
(4)
Example 3.2. From Figure 1, an agent might say
My interest is Disease except HeartDisease. That is,
we may take I
c
(Disease) = 1.2 (i.e. i
c
(Disease) =
1.2) and I
c
(HeartDisease) = 0 (i.e. i
c
(Disease) =
1.2 0 and i
c
(Heart) = 0). Taking as
max
yields
i
c
(Disease) = 1.2 and i
c
(Heart) = 0. It also yields the
same results by taking as
first
.
Example 3.3. From Figure 1, an agent might say
My concern is nothing except HeartDisease. That is,
we may take I
c
(>) = 0 (i.e. i
c
(Disease) = 0,
i
c
(Tissue) = 0, and i
c
(Heart) = 0) and
I
c
(HeartDisease) = 1 (i.e. i
c
(Disease) = 0 1
and i
c
(Heart) = 0 1). Taking as
max
yields
i
c
(Disease) = 1, i
c
(Tissue) = 0, and i
c
(Heart) = 1. It
also yields the same results by taking as
last
.
Now, we discuss our second concern on the ap-
plication of I
c
. Let us consider the following pref-
erence expression of an agent: I
c
(Pericarditis) = 1.2
and I
c
(Endocarditis) = 1.6. One may notice that both
use the primitive concept name Disease in common.
Now, a natural question to ask is how a concept im-
portance value should be propagated since a propaga-
tion may cause an inconsistency of preference values
for a primitive concept name, such as Disease in this
example. This requires further work to study. How-
ever, one simple way for handling this problem is to
prevent a mapping leading to this situation. Instead,
an agent has to tune primitive concept names via the
primitive concept importance i
c
individually.
Lastly, we contemplate our third concern. That
is, what happens if a defined concept name C
1
is
defined on I
c
and there exists another defined con-
cept name C
2
such that C
1
T
C
2
? A natural way
for handling this problem is to treat C
2
in the same
way as C
1
(because they are equivalent). In particular,
C
1
,C
2
CN
def
(T ) : C
1
T
C
2
I
c
(C
1
) = I
c
(C
2
).
Nevertheless, this also requires further work to ex-
plore other possibilities for coping with this prob-
lem and investigate desired properties the notion
π
T
should hold when it is used with I
c
.
3.2 Tuning i
r
Let us remind that i
r
is a function which maps a role
name r RN to a value x [0, 2]. Its primary motiva-
tion is to define a user-identified importance value for
an individual role name. A distinguished characteris-
tic of i
r
to i
c
is that, not only restricted to primitive
ones, ones may also define an importance on defined
role names. We bear this understanding on the devel-
opment of a strategy to tune i
r
as follows.
Our primary motivation of providing a strategy to
help tuning i
r
is similar to that one of i
c
. That is,
realistic ontologies are complex – consisting in plenty
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
291
of role names. An intuitive way to simplify the task of
tuning i
r
is to proceed on a more general role name.
We note that, suppose r v s T , a role s is said to be
more general than a role r. This intuition shapes our
development as follows:
Definition 3.3. Let RN(T ) be a set of role names
occurring in T . Then, a propagation for role impor-
tance is a partial function I
r
: RN
0
[0, 2], where
RN
0
RN(T ), such that a mapping n of I
r
on X (i.e.
I
r
(X) = n) is inductively defined as follows:
5
.
1. X
0
RN(T ): (X
0
v X T i
r
(X) = n and
I
r
(X
0
) = n); and
2. X
0
RN(T ): (X
0
v X 6∈ T i
r
(X) = n).
There are a few concerns that we should take into
account, i.e. (1) inconsistent preferences of roles oc-
curring on the same branch of the role hierarchy; and
(2) expressing preferences when a TBox T contains
equivalent role names. We discuss these in order.
Let us take a look on our first concern through
the following preference expression (according to
an ontology given in Example 1.1): my role im-
portance goes through canMoveWithLegs, especially
canWalk. Suppose we take I
c
(canMoveWithLegs) =
1.2 and I
c
(canWalk) = 1.3. Here, canWalk is rede-
fined on i
r
twice. Similar to I
c
, we handle this prob-
lem with the use of operators : [0, 2]
2
[0, 2].
Definition 3.4. Let r RN(T ) be a set of role names
occurring in T and x
0
, x
1
[0, 2]. Also, let i
r
(r) = x
0
be the previous mapping on r. We compute a new
mapping i
r
(r) = x
1
as follows:
i
r
(r) =
(
x
1
if i
r
is not defined on r
x
0
x
1
otherwise
(5)
The operator remains abstract here as its concrete
operators may vary on the context of use and may be
defined in the same sense as I
c
(e.g. Equation 2 to
4). For example, an agent may prefer to take the last
mapping when that agent says exceptional cases (e.g.
r except s where r R
s
) in order to suppress the pre-
viously propagated value. Also, an agent may prefer
to take the last mapping when that agent would like
to emphasize some special circumstances (e.g. r es-
pecially s where r R
s
) in order to suppress the pre-
viously propagated value.
Example 3.4. From Example 1.1, an agent might say
My interest is canMoveWithLegs except canWalk.
That is, we may take I
r
(canMoveWithLegs) = 1.2
(i.e. i
r
(canMoveWithLegs) = 1.2 and i
r
(canWalk) =
1.2) and I
r
(canWalk) = 0 (i.e. i
r
(canWalk) = 1.2
5
Later, we discuss some restrictions the readers should
take into account when the notion I
r
is employed.
2). Using
first
for yields i
r
(canMoveWithLegs) =
1.2 and i
r
(canWalk) = 0.
Example 3.5. From Example 1.1, an agent might
say My interest is canMoveWithLegs, especially
canWalk. Let us take I
c
(canMoveWithLegs) = 1.2
(i.e. i
r
(canMoveWithLegs) = 1.2 and
i
r
(canWalk) = 1.2) and I
c
(canWalk) = 1.3 (i.e.
i
r
(canWalk) = 1.2 1.3). Using
last
for yields
i
r
(canMoveWithLegs) = 1.2 and i
r
(canWalk) = 1.3.
Lastly, we discuss the second concern. That is,
what happens if a defined role name r
1
is defined on
I
r
and there exists another defined role name r
2
such
that r
1
v
T
r
2
and r
2
v
T
r
1
? Similar to our basic
handling of this case in I
c
, we recommend to treat
r
2
in the same way as r
1
(because they are equiva-
lent). Nevertheless, this also requires further work to
explore other possibilities for coping with this prob-
lem and investigate desired properties the notion
π
T
should hold when it is used with I
r
.
3.3 Tuning s
c
In this subsection, we present a strategy for tuning
primitive concepts similarity. If an ABox A is pre-
sented, then we can induce the canonical interpreta-
tion I
A
from A to calculate primitive concepts simi-
larity for all possible primitive concept pairs. Suppose
that I
A
is constructed and let A, B CN
pri
(T ), we es-
tablish the following calculation for the function s
c
.
s
c
(A, B) =
(
1 if A
I
A
= B
I
A
=
/
0
|A
I
A
B
I
A
|
|A
I
A
B
I
A
|
otherwise
(6)
where | · | represents the set cardinality.
Intuitively, Equation 6 computes the commonality
of both primitive concept names. Since O
med
does not
contain an ABox A, let us use a handcraft ontology to
exemplify the calculation.
Example 3.6. Let a family ontology O = hT , Ai in
which T is defined as follows:
Grandfather Man u child.Parent
Parent Person u child.Person
Man Male u Person
Let an ABox A is defined as follows:
child(john, elise) child(emma, watson)
Person(john) Person(elise)
Person(emma) Person(watson)
Male(john) Male(watson)
Thus,
I
A
= {elise, john, emma, watson},
Person
I
A
= {john, elise, emma, watson}, Male
I
A
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
292
= {john, watson}, and s
c
(Person, Male) =
|john,watson|
|john,elise,emma,watson|
=
1
2
= 0.5.
3.4 Tuning s
r
This subsection presents a strategy for tuning primi-
tive roles similarity. Indeed, we attempt in the similar
fashion as what we do for s
c
. That is, we use the
canonical interpretation I
A
to obtain primitive roles
similarity. Let r, s RN
pri
(T ) and define operators ·
f
and ·
s
for any primitive role r as r
f
= {x | (x, y) r
I
A
}
and r
s
= {y | (x, y) r
I
A
}, respectively, then:
s
r
(r, s) =
1 if r
I
A
= s
I
A
=
/
0
λ ·
|r
f
s
f
|
|r
f
s
f
|
+(1 λ) ·
|r
s
s
s
|
|r
s
s
s
|
otherwise
(7)
where 0 < λ < 1 and | · | represents the set cardinality.
Intuitively, Equation 7 is defined as the weighted
sum of the commonality on the first arguments of
roles and the commonality on the second arguments
of roles. It is recommended to set the weight λ =
|r
f
s
f
|
|r
f
s
f
|+|r
s
s
s
|
, i.e. the proportion of all individuals ap-
pearing on the first arguments to all individuals ap-
pearing on both arguments. The following example
exemplifies the calculation.
Example 3.7. Let a family ontology O = hT , Ai in
which T is defined as follows:
Parent Person u child.Person
BrotherSister Person u sibling.Person
Let an ABox A is defined as follows:
sibling(john, max) sibling(yok, watson)
child(emma, yok) child(john, elise)
child(emma, watson) Person(john)
Person(elise) Person(emma)
Person(watson) Person(max)
Person(yok)
Thus,
I
A
= {elise, john, emma, watson,
max, yok}, child
f
= {emma, john}, sibling
f
=
{yok, john}, child
s
= {yok, watson, elise}, sibling
s
=
{watson, max}, and s
r
(child, sibling) =
3
7
·
1
3
+
4
7
·
1
4
0.48.
3.5 Tuning d
The primary motivation of this aspect is to capture an
expression of total expression on a role beyond a cor-
responding nested concept (Racharak et al., 2016a).
Hence, tuning this aspect may requires skilled do-
main expertise. For example, SNOMED ontology
engineers realize that roleGroup is used to nestedly
group existential restrictions; hence, it can uninten-
tionally increase the degree of similarity due to role
commonality. Considering this fact, they may set
d(roleGroup) = 0. This shows that role discount fac-
tor of different role names may be independent. How-
ever, the same strategy as I
r
can be employed to com-
fort on configuring this aspect, i.e. a propagation for
role discount factor via a more general role name.
4 APPLYING PROPOSED
STRATEGIES TO MEASURE
ELH CONCEPTS
In this section, we show an applicability of the pro-
posed strategies for tuning preference profile π to be
used with the measure sim
π
(Racharak et al., 2016b).
We note that sim
π
is an instance of
π
T
(Definition
2.3) for DL ELH . Using sim
π
requires that concept
definitions in a TBox T must be fully expanded, i.e.
for each defined concept name A CN
def
(T ), such
that A D, we simply replace A with D wherever it
occurs in C and continue to recursively expand D. If
A is of the form A v D, then we replace A with X uD
such that X is a fresh concept wherever A occurs in C
and recursively expand D. We note that X represents
the primitiveness of A, i.e. the unspecified character-
istics that differentiate it from D.
For the purpose of self-containment, we include
the original definition of homomorphism degree un-
der preference profile hd
π
and the similarity degree
under preference profile sim
π
here.
In order to consider all aspects of preference pro-
file, we have presented a total importance function as
ˆ
i : CN
pri
RN [0, 2]
ˆ
i(x) =
i
c
(x) if x CN
pri
and i
c
is defined on x
i
r
(x) if x RN and i
r
is defined on x
1 otherwise
(8)
A total similarity function is also presented as
ˆ
s : (CN
pri
× CN
pri
) (RN
pri
× RN
pri
) [0, 1] using
primitive concepts similarity and primitive roles sim-
ilarity.
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
293
ˆ
s(x, y) =
1 if x = y
s
c
(x, y) if (x, y) CN
pri
× CN
pri
and s
c
is defined on (x, y)
s
r
(x, y) if (x, y) RN
pri
× RN
pri
and s
r
is defined on (x, y)
0 otherwise
(9)
Similarly, a total role discount factor function is pre-
sented in the following in term of a function
ˆ
d : RN
[0, 1] based on role discount factor.
ˆ
d(x) =
(
d(x) if d is defined on x
0.4 otherwise
(10)
Let us note that the default value of Equation 8 - 10
is set according to the default preference profile π
0
(Definition 2.2).
Let C Con(E LH ) be a fully expanded concept
to the form:
P
1
u · · · u P
m
u r
1
.C
1
u · · · u r
n
.C
n
where P
i
CN
pri
, r
j
RN, C
j
Con(ELH ) in the
same format, 1 i m, and 1 j n. The set
P
1
, . . . , P
m
and the set r
1
.C
1
, . . . , r
n
.C
n
are denoted
by P
C
and E
C
, respectively. An E LH concept de-
scription can be structurally transformed into the cor-
responding ELH description tree. The root v
0
of the
ELH description tree T
C
has {P
1
, . . . , P
m
} as its la-
bel and has n outgoing edges, each labeled with r
j
to
a vertex v
j
for 1 j n. Then, a subtree with the
root v
j
is defined recursively relative to the concept
C
j
. Let π = hi
c
, i
r
, s
c
, s
r
, di be a preference profile.
The homomorphism degree under preference profile
π can be formally defined as follows:
Definition 4.1 ((Racharak et al., 2016b)) . Let
T
ELH
be a set of all ELH description trees and
T
C
, T
D
T
ELH
corresponds to two ELH concept
names C and D, respectively. The homomorphism de-
gree under preference profile π is a function hd
π
:
T
ELH
× T
ELH
[0, 1] defined inductively as fol-
lows:
hd
π
(T
D
, T
C
) = µ
π
· p-hd
π
(P
D
, P
C
)
+ (1 µ
π
) · e-set-hd
π
(E
D
, E
C
), (11)
where
µ
π
=
1 if
AP
D
ˆ
i(A)
and
r.X E
D
ˆ
i(r) = 0
AP
D
ˆ
i(A)
AP
D
ˆ
i(A)+
r.XE
D
ˆ
i(r)
otherwise;
(12)
p-hd
π
(P
D
, P
C
) =
1 if
AP
D
ˆ
i(A) = 0
0 if
AP
D
ˆ
i(A) 6= 0 and
BP
C
ˆ
i(B) = 0
p
π
(P
D
, P
C
) otherwise,
(13)
where
p
π
(P
D
, P
C
) =
AP
D
ˆ
i(A) · max{
ˆ
s(A, B) : B P
C
}
AP
D
ˆ
i(A)
;
(14)
e-set-hd
π
(E
D
, E
C
) =
1 if
r.X E
D
ˆ
i(r) = 0
0 if
r.X E
D
ˆ
i(r) 6= 0
and
s.Y E
C
ˆ
i(s) = 0
e
π
(E
D
, E
C
) otherwise,
(15)
where
e
π
(E
D
, E
C
) =
r.X E
D
ˆ
i(r) · max{e-hd
π
(r.X, ε
j
) : ε
j
E
C
}
r.X E
D
ˆ
i(r)
(16)
with ε
j
existential restriction; and
e-hd
π
(r.X, s.Y ) = γ
π
(
ˆ
d(r)+(1
ˆ
d(r))·hd
π
(T
X
, T
Y
))
(17)
where γ
π
=
1 if
r
0
R
r
ˆ
i(r
0
) = 0
r
0
R
r
ˆ
i(r
0
)·max{
ˆ
s(r
0
,s
0
):s
0
R
s
}
r
0
R
r
ˆ
i(r
0
)
, otherwise.
(18)
Intuitively, Equation 11 is defined as the weighted
sum of the degree under π of primitive concepts and
the degree under π of matching edges. Equation 12
indicates the weight of primitive concept names w.r.t.
the importance function. Equation 13 calculates the
proportion of best similarity between primitive con-
cept names. Similarly, Equation 15 calculates the pro-
portion of best similarity between existential informa-
tion from Equation 17 and Equation 18. Equation 17
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
294
calculates the degree of similarity between matching
edges. Finally, Equation 18 calculates the proportion
of best similarity between role names.
Let C and D be fully expanded ELH concept
names, T
C
and T
D
be the corresponding description
trees, and π = hi
c
, i
r
, s
c
, s
r
, di be a preference profile.
The following definition formally describes the E LH
similarity degree under preference profile π.
Definition 4.2 ((Racharak et al., 2016b)) . The
ELH similarity degree under preference profile π be-
tween C and D (denoted by sim
π
(C, D)) is defined as
follows:
sim
π
(C, D) =
hd
π
(T
C
, T
D
) + hd
π
(T
D
, T
C
)
2
(19)
Intuitively, the degree of similarity under prefer-
ence profile of two concepts is the average of the de-
gree of having homomorphisms under preference pro-
file in both directions. We note that sim
π
(C, D) = 1
indicates that C and D are total similarity under a par-
ticular π and sim
π
(C, D) = 0 indicates total dissimi-
larity between C and D under a particular π.
4.1 A Simple Methodology
Now, we are ready to discuss a simple methodol-
ogy for reconciling the previously proposed strate-
gies with the measure sim
π
(Definition 4.2). Section 3
shows that each aspect of preference profile may need
different strategies for tuning. For example, i
c
may be
tuned via a defined concept name using a propagation
for primitive concept importance I
c
whereas i
r
may
be tuned via a more general role name using a prop-
agation for role importance I
r
. Also, both s
c
and s
r
may employ the canonical interpretation I
A
to initial-
ize values. In the following, we explain procedural
steps that the readers may follow to tune preference
profile for their use. These steps also hint a system
flow of similarity-based under the agent’s profile ap-
plications, such as the best matching concept under
the agent’s profile application.
1. An agent may start with tuning each aspect of
preference profile individually;
2. To help tuning i
c
, a system may present the con-
cept hierarchy w.r.t. an ontology. Then, an agent
indirectly specify primitive concept names via a
defined concept name depicted on the hierarchy
with the notion I
c
(cf. Definition 3.1 and Defini-
tion 3.2). Some patterns of an agent’s utterance
may be associated with certain operators, e.g.
(a) We may associate A especially B with
first
,
where depth(A) < depth(B) and depth(X ) is the
depth of X on the concept hierarchy;
(b) We may associate A except B with
first
, where
depth(A) < depth(B) and C
1
6= >;
(c) We may associate > except B with
last
; and
(d) Otherwise, the agent-defined default concrete
operator is used;
3. To help tuning i
r
, a system may present the role
hierarchy w.r.t. an ontology. Then, an agent indi-
rectly specify role names via a more general role
name name depicted on the hierarchy with the
noion I
r
(cf. Definition 3.3 and Definition 3.4).
Similarly, some patterns of an agent’s utterance
may be associated with certain operators, e.g.
(a) We may associate r especially s with
last
,
where r R
s
;
(b) We may associate r except s with
last
, where
r R
s
; and
(c) Otherwise, the agent-defined default concrete
operator is used;
4. To help tuning s
c
and s
r
, a system may con-
struct the canonical interpretation, which is in-
duced from A. Then, each initial value for all
possible primitive concept pairs and primitive role
pairs is calculated according to Equation 6 and
Equation 7, respectively;
5. An agent may refine the agent’s preference profile
if that agent wishes.
We exemplify the methodology in its applicable
use cases, such as trip planning (Example 4.1).
Example 4.1. (Continuation from Example 1.1) We
expand each definition in T as follows:
ActivePlace X uPlace u canWalk.Trekking
u∃canSail.Kayaking
Mangrove Y u Place u canWalk.Trekking
Beach Z u Place u canSail.Kayaking
where X, Y , and Z are fresh primitive concept names.
Furthermore, R
canWalk
= {t, cMWL}
6
and R
canSail
=
{t, cTWS} where t and u are also fresh primitive role
names.
Let an ABox A be defined as follows:
cMWL(p
2
,t
1
) cTWS(p
3
, k
1
)
canWalk(p
2
,t
1
) canSail(p
3
, k
1
)
Trekking(t
1
) Kayaking(k
1
)
Place(p
1
) Place(p
2
)
Place(p
3
) Mangrove(p
2
)
Beach(p
3
)
To query for a desired place, an agent needs to
express his preferences. Suppose the agent says
6
Obvious abbreviations are used here for the sake of suc-
cinctness.
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
295
My interest is a place where I can travel with
by feet, especially walking, i.e. i
c
(Place) = 1.5,
I
r
(canMoveWithLegs) = 1.5, and I
r
(canWalk) =
1.8. Also, it yields i
r
(canMoveWithLegs) = 1.5 and
i
r
(canWalk) = 1.5
last
1.8 = 1.8.
Constructing the canonical interpreta-
tion from A, we obtain
I
A
= {p
1
, p
2
,
p
3
, t
1
, k
1
}, s
c
(Trekking, Kayaking) = 0, and
s
r
(canMoveWithLegs, canTravelWithSails) = 0.
Let ActivePlace, Mangrove, Place, Trekking,
Kayaking, canWalk, and canSail are rewritten shortly
as AP, M, P, T, K, cW, and cS, respectively. Using
Definition 4.1, hd
π
(T
AP
, T
M
)
= (
2.5
5.3
) · p-hd
π
(P
AP
, P
M
) + (
2.8
5.3
) · e-set-hd
π
(E
AP
, E
M
)
= (
2.5
5.3
) · (
i(X)·max{s(X,Y ),s(X,P)}+i(P)·max{s(P,Y),s(P,P)})
i(X)+i(P)
)
+(
2.8
5.3
) · e-set-hd
π
(E
AP
, E
M
)
= (
2.5
5.3
)(
1·max{0,0}+1.5·max{0,1}
1+1.5
)
+(
2.8
5.3
) · e-set-hd
π
(E
AP
, E
M
)
= (
2.5
5.3
)(
1.5
2.5
) + (
2.8
5.3
)
h
i(cW)·max{e-hd
π
(cW.T,cW,T)}+1·0
i(cW)+i(cS)
i
= (
2.5
5.3
)(
1.5
5.3
) + (
2.8
5.3
)
1.8·1+1·0
1+1.8
0.623
Following the same step, we obtain hd
π
(T
M
, T
AP
)
0.767. Hence, sim
π
(M, AP) 0.695 by using Defini-
tion 4.2. Also, we obtain hd
π
(T
AP
, T
B
) 0.472 and
hd
π
(T
B
, T
AP
) 0.714. Hence, sim
π
(B, AP) 0.593.
The fact that sim
π
(M, AP) > sim
π
(B, AP) corre-
sponds to the agent’s perception.
5 RELATIONSHIP TO
LEARNING-BASED APPROACH
Our proposed development uses the canonical inter-
pretation I
A
to compute numerical values for map-
pings on s
c
(cf. Subsection 3.3) and s
r
(cf. Subsection
3.4). Its drawback is that an existence of the canon-
ical interpretation I
A
is required. This section rather
discusses an alternative approach to obtain values for
mappings on s
c
and s
r
.
In addition to our proposed logic-based approach,
another natural way to configure both s
c
and s
r
is
to employ existing machine learning techniques on a
large corpus. For example, one may use Word2vec
(Mikolov et al., 2013) with a large corpus of text to
produce a vector space. Each word in the corpus will
be assigned by a corresponding vector in the space.
Word vectors are positioned in the vector space such
that words sharing common features in the corpus are
located in close proximity to one another in the space.
This characterization can later be converted into ele-
ments of the mapping s
c
and s
r
. Reconciling an on-
tology with machine learning techniques to improve
an application of
π
T
is interesting but is outside the
scope of this paper. We leave this as a future task.
6 RELATED WORK
While there has been substantial work on concept
similarity measures in the context of DLs, the topic
of concept similarity measure under an agent’s prefer-
ences remains relatively unaddressed. Notable excep-
tions include (Tongphu and Suntisrivaraporn, 2015;
Lehmann and Turhan, 2012); however, measures pre-
sented in these papers may not include preferential
aspects evidently in the formal definition. We discuss
the differences of ours to others in the following.
As similarity may be subjective, the techniques in-
volved in concept similarity measure can be classified
into two main classes: ones which address the prob-
lem under an agent’s preferences, e.g. sim
π
(orig-
inally introduced in (Racharak et al., 2016b)), and
ones which do not, e.g. (Janowicz and Wilkes, 2009;
Racharak and Suntisrivaraporn, 2015; D’Amato et al.,
2006; Fanizzi and D’Amato, 2006; D’Amato et al.,
2009; D’Amato et al., 2008). The measure sim
π
gen-
eralizes the notion of homomorphism structural sub-
sumption with an aim to develop a similarity mea-
sure under preference profile for DL ELH . As pre-
viously mentioned, (Tongphu and Suntisrivaraporn,
2015; Lehmann and Turhan, 2012) may not include
preferential aspects evidently in the formal definition;
however, their approaches share some viewpoints in
common to preference profile. For instance, (Tong-
phu and Suntisrivaraporn, 2015) provides some facili-
ties similar to i
c
and d whereas (Lehmann and Turhan,
2012) provides some facilities similar to i
c
, s
c
, and
s
r
. We refer the readers to (Racharak et al., 2016a;
Racharak et al., 2016b) for the detailed discussion.
Speaking out in the context of DLs, we may
classify techniques in the other way round, i.e.
structure-based measure and interpretation-based
measure. Structure-based measure, e.g. (Janowicz
and Wilkes, 2009; Racharak and Suntisrivaraporn,
2015; D’Amato et al., 2006; Fanizzi and D’Amato,
2006; Tongphu and Suntisrivaraporn, 2015; Lehmann
and Turhan, 2012; Racharak et al., 2016b), is
defined using the syntax of concepts being mea-
sured. On the other hand, interpretation-based mea-
sure, e.g. (D’Amato et al., 2009; D’Amato et al.,
2008), is defined using interpretations and cardinal-
ity. Some measures also include elements of both,
e.g. (D’Amato et al., 2006; Fanizzi and D’Amato,
2006) use structure to measure concepts but use the
canonical interpretation I
A
to measure similarity of
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
296
Figure 3: A mock-up of the best-matching concepts under the agent’s profile application.
primitive concept names. The measure sim
π
per se
is categorized as a structure-based measure; however,
reconciling sim
π
with our strategies to help tuning
s
c
and s
r
may be considered as the last category as
it uses the canonical interpretation I
A
for measuring
similarity of primitive concept names and similarity
of primitive role names.
This work is an extension of the original sim
π
(Racharak et al., 2016b) in which we investigate and
formalize the task of configuring the preference func-
tions based on the information defined in a TBox and
an ABox (cf. Section 3). We also show that the pro-
posed strategies can be reconciled with the original
development, i.e. sim
π
(cf. Section 4).
7 DISCUSSION AND FUTURE
RESEARCH
As realistic ontologies are generally complex con-
sisting in plenty of concept names and role names,
having some strategies to tune a measure helps ontol-
ogy engineers, researchers, and application users to
use a measure for similarity-based under the agent’s
profile applications. That is, instead of specifying
each aspect of preference profile individually and
manually, an agent may automatically assign an im-
portance of each primitive concept name through a
defined concept name with I
c
. Similarly, an agent
may automatically assign an importance of each role
name through a more general role name with I
r
.
However, these notions have some restrictions and we
discuss these in Subsection 3.1 and Subsection 3.2,
respectively. If an ABox is presented, the canonical
interpretation can be induced and be used to further
compute s
c
and s
r
for each primitive concept pair and
primitive role pair (cf. Subsection 3.3 and Subsection
3.4). In any cases, these strategies are recommended
to use for the initial preference tuning and these val-
ues may be refined wherever the agent wishes.
We also present a simple guideline to implement
similarity-based under the agent’s profile applications
(cf. Subsection 4.1). As exhibited by the guideline, a
system may depict the concept hierarchy and the role
hierarchy w.r.t. an ontology to let an agent fine tune
via I
c
and I
r
, respectively. Figure 3 shows a mock-up
of the best-matching concept under the agent’s pro-
file application. In this mock-up, we permit an agent
to identify his preferences through the notion I
c
by
highlighting concept names occurring on the hierar-
chy. We note that this mock-up does not show all the
strategies we have discussed in this work. Also, it
uses
max
to handle conflicting values on i
c
.
Currently, we are under an implementation of the
best-matching application under the agent’s profile
using our extended measure sim
π
. There are several
possible directions for the theoretical future research.
Tuning Agent’s Profile for Similarity Measure in Description Logic ELH
297
Firstly, our current strategies cannot be used to ex-
press complex preferences, such as multi-dimensional
preferences. Hence, it appears to be a natural step
to develop a high-level language for the specification
of an agent’s preferences in the context of similarity-
based problems. Secondly, we are interested to ex-
tend the notion of preference profile to support a more
expressive DL family, e.g. universal restriction, con-
cept negation, and also, to support an ABox. Thirdly,
we intend to devise a concept similarity measure un-
der preference profile which can handle more expres-
sive DLs. Finally, we intend to employ our devel-
oped notion of concept similarity measure under pref-
erence profile toward a system of analogical reason-
ing. As we have developed an argument-based logic
programming for analogical reasoning in (Racharak
et al., 2016c), it would be interesting to connect these
two research studies.
ACKNOWLEDGEMENTS
The authors would like to thank Prachya Boonkwan
for his proofreading and useful comments. This re-
search is part of the JAIST-NECTEC-SIIT dual doc-
toral degree program.
REFERENCES
Ashburner, M., Ball, C. A., Blake, J. A., Botstein, D.,
Butler, H., Cherry, J. M., Davis, A. P., Dolinski, K.,
Dwight, S. S., Eppig, J. T., Harris, M. A., Hill, D. P.,
Issel-Tarver, L., Kasarskis, A., Lewis, S., Matese,
J. C., Richardson, J. E., Ringwald, M., Rubin, G. M.,
and Sherlock, G. (2000). Gene Ontology: tool for the
unification of biology. Nature Genetics, 25(1):25–29.
Baader, F., Calvanese, D., McGuinness, D. L., Nardi, D.,
and Patel-Schneider, P. F. (2010). The Description
Logic Handbook: Theory, Implementation and Appli-
cations. Cambridge University Press, New York, NY,
USA, 2nd edition.
D’Amato, C., Fanizzi, N., and Esposito, F. (2006). A dis-
similarity measure for alc concept descriptions. In
Proceedings of the 2006 ACM Symposium on Applied
Computing, pages 1695–1699.
D’Amato, C., Fanizzi, N., and Esposito, F. (2009). A se-
mantic similarity measure for expressive description
logics. In CoRR, abs/0911.5043.
D’Amato, C., Staab, S., and Fanizzi, N. (2008). On the in-
fluence of description logics ontologies on conceptual
similarity. In Proceedings of Knowledge Engineering:
Practice and Patterns, pages 48–63.
Euzenat, J. and Valtchev, P. (2004). Similarity-based on-
tology alignment in OWL-lite. In de M
´
antaras, R. L.
and Saitta, L., editors, Proceedings of the 16th Euro-
pean Conference on Artificial Intelligence (ECAI-04),
pages 333–337. IOS Press.
Fanizzi, N. and D’Amato, C. (2006). A similarity measure
for the aln description logic. In Proceedings of CILC
2006 - Italian Conference on Computational Logic,
pages 26–27.
Grau, B. C., Horrocks, I., Motik, B., Parsia, B., Patel-
Schneider, P., and Sattler, U. (2008). Owl 2: The next
step for owl. Web Semant., 6(4):309–322.
Group, W. O. W. (2012). OWL 2 web ontology language.
document overview (second edition). W3C recom-
mendation, W3C.
Janowicz, K. and Wilkes, M. (2009). Sim-dla: A novel
semantic similarity measure for description logics re-
ducing inter-concept to inter-instance similarity. In
Proceedings of the 6th European Semantic Web Con-
ference on The Semantic Web: Research and Applica-
tions, pages 353–367.
Lehmann, K. and Turhan, A.-Y. (2012). A framework for
semantic-based similarity measures for elh-concepts.
In del Cerro, L. F., Herzig, A., and Mengin, J., editors,
JELIA, volume 7519 of Lecture Notes in Computer
Science, pages 307–319. Springer.
Mikolov, T., Chen, K., Corrado, G., and Dean, J. (2013).
Efficient estimation of word representations in vector
space. CoRR, abs/1301.3781.
Racharak, T. and Suntisrivaraporn, B. (2015). Similar-
ity measures for F L
0
concept descriptions from an
automata-theoretic point of view. In Information and
Communication Technology for Embedded Systems
(IC-ICTES), 2015 6th International Conference of,
pages 1–6.
Racharak, T., Suntisrivaraporn, B., and Tojo, S. (2016a).
Identifying an Agent’s Preferences Toward Similar-
ity Measures in Description Logics, pages 201–208.
Springer International Publishing, Cham.
Racharak, T., Suntisrivaraporn, B., and Tojo, S. (2016b).
sim
π
: A concept similarity measure under an agent’s
preferences in description logic ELH . In Proceed-
ings of the 8th International Conference on Agents
and Artificial Intelligence, pages 480–487.
Racharak, T., Tojo, S., Hung, N. D., and Boonkwan, P.
(2016c). Argument-based logic programming for
analogical reasoning. In Proceeding of Tenth In-
ternational Workshop on Juris-informatics (JURISIN
2016).
Stearns, M. Q., Price, C., Spackman, K. A., and Wang, A. Y.
(2001). SNOMED clinical terms: overview of the de-
velopment process and project status. Proceedings /
AMIA ... Annual Symposium. AMIA Symposium, pages
662–666.
Tongphu, S. and Suntisrivaraporn, B. (2015). Algorithms
for measuring similarity between elh concept descrip-
tions: A case study on snomed ct. Journal of Comput-
ing and Informatics (accepted on May 7; to appear).
ICAART 2017 - 9th International Conference on Agents and Artificial Intelligence
298