The notion of homomorphism degree was origi-
nally introduced in (Suntisrivaraporn, 2013) and em-
ployed as the heart of the similarity measure for the
DL EL. This has been extended to ELH and con-
tinuously studied in (Tongphu and Suntisrivaraporn,
2014; Tongphu and Suntisrivaraporn, 2015).
Racharak and Suntisrivaraporn suggested two new
notions of similarity for the DL F L
0
(Racharak and
Suntisrivaraporn, 2015). Both the skeptical and cred-
ulous similarity measures are derived from the known
structural characterization subsumption through in-
clusion of regular languages.
The similarity measure presented in this paper is
similar to those reported in (Tongphu and Suntisri-
varaporn, 2014; Suntisrivaraporn, 2013). It however
focuses on the strictly more expressive DL and em-
ploys generalizations of the normalization and char-
acterization from (Baader and K¨usters, 2006).
7 DISCUSSIONS AND FUTURE
WORKS
This paper presents a new notion of concept similarity
for the DL ALEH w.r.t. an unfoldable terminology
and suggests a way to approximate concept similarity
for the more expressive ALC H . At the heart of the
measure is the calculation of the degree of homomor-
phism to and from between two description trees. To
allow this, we ﬁrst review and extend the known nor-
malization and homomorphism to take into account
also role hierarchy axioms. The proposed similarity
measure can be regarded as an extension of the sim-
ilarity measure sim for the EL family (Suntisrivara-
porn, 2013; Tongphu and Suntisrivaraporn, 2015).
There are various directions for future works. One
could try to evaluate the proposed measure on appro-
priate ontologies from real-world domains. Similar to
the experiments on SNOMED CT reported in (Tong-
phu and Suntisrivaraporn, 2015), a similar setting can
be carried out. Besides, more expressive ontologies
that make use of the universal quantiﬁcation such as
GALEN could be experimented upon. It can be ex-
pected to ﬁnd out new hidden knowledge in the on-
tology that could not have been done before with the
mere standard reasoner. Another useful application
is a measure of similarity between diseases proposed
in (Mathur and Dinakarpandian, 2012). The appli-
cation has shown useful cases in similarity measure
processes underlying each disease for more accurate
unknown disease prediction.
Concerning the choice of representation lan-
guage, it is an obvious future work to explore non-
approximate similarity measure for ALC by investi-
gating under scrutiny into the original tableau algo-
rithm. Another direction for future work could be
to compare the measure presented in this paper to
those two notions of similarity for F L
0
introduced in
(Racharak and Suntisrivaraporn, 2015). Since F L
0
is a sub-logic of ALEH and as such sim
ALEH
is
applicable also to F L
0
, it is interesting to explore
whether sim
ALEH
is stronger (see (Racharak and
Suntisrivaraporn, 2015)) than the skeptical and cred-
ulous similarity measures.
ACKNOWLEDGEMENTS
This research is partially supported by Thammasat
University Research Fund under the TU Research
Scholar, Contract No. TOR POR 1/13/2558; the Cen-
ter of Excellence in Intelligent Informatics, Speech
and Language Technology, and Service Innovation
(CILS), Thammasat University; and the National Re-
search University (NRU) project of Thailand Ofﬁce
for Higher Education Commission.
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