Repai ing Concep ual Rela ions in On ologies by
means o an In e ac i e Visual Reasoning:
Cogni i e and Design P inciples
Gonzalo A. A anda-Co al
Dep . o In o ma ion Technology
Uni e sidad de Huel a
Palos de La F on e a, Spain
Email:[email p o ec ed]
Joaqu´
ın Bo ego-D´
ıaz
Dep . Compu e Science and AI
Uni e sidad de Se illa
Se illa, Spain
Email:[email p o ec ed]
An onia M. Ch´
a ez-Gonz´
alez
Dep . Compu e Science and AI
Uni e sidad de Se illa
Se illa, Spain
Email: cha[email p o ec ed]
Abs ac —The echnologies o isual ep esen a ion a e a g ea
help o unde s anding i ems o in o ma ion and he ela ions
among hem, especially, o non-expe use s on Knowledge Based
Sys ems, e.g. on ologies, which ep esen a wo ld ha can e ol e
and, he e o e, has o be e en ually e ined. To ensu e a cogni i e
communica ion soundness, we mus in eg a e in o solu ions bo h,
usabili y o hese non-expe use s and a logical accu acy on
all in ol ed elemen s. In his pape , he design p inciples o a
ool o he isual epai o anomalies in consis en on ologies
is p esen ed. I helps use s o ob ain an on ological ag eemen
be ween his men al model o he concep s in o discou se domain
and he in ended model o he on ology ( ha is supposed o be
consis en ).
I. INTRODUCTION
The design o A i icial In elligence (AI) ools o ep esen
and p ocess knowledge is a pe sis en goal which mus o deal
wi h challenging p oblems such as he luidi y o knowledge’s
seman ics i sel . Ha ing in mind his idea, in gene al, use s do
no unde s and Knowledge Enginee ing Techniques and Tools
and, in o de o popula ize he use o such skills, esea che s
ha e o b idge he gap be ween ools and end-use s. This is
usually done by designing isual in e aces [7], [22].
A pa icula ly in e es ing case occu s when dealing wi h
p oblems o seman ic in e ope abili y be ween agen s/use s.
Tha is, when agen s need o sha e knowledge and hey ha e
o unde and and accep i , in o de o wo k wi h. In his case,
on ologies play a key ole being used o agging me ada a,
in an e ec i e way, wi h consensus and p ope ly unde s ood
by all. Howe e , his equi emen becomes a challenge when
agen s a e illi e acies in Seman ic Web echnologies.
The cogni i e gap, which a ises be ween he model ha
agen s hink i is and he model which i eally is, mus be
a oided i we wan ha communica ion and in e ac ion a e
cogni i ely sound. In ac , his p oblem mus be sol ed wi h
cogni i e in e aces ha allow use s bo h o unde s and and o
adjus in ol ed on ologies. Visual me apho s a e a powe ul
sou ce o me hodologies o p o iding solu ions.
In his pape we add ess he p oblem o isualizing he
ep esen a ion and he e ec o he au oma ed easoning on
on ologies ( hei Desc ip ion Logics ep esen a ion [14]). This
issue may include p ac ical managemen o on ologies, such as
ex ension, e inemen and e sioning echniques. The design
p inciples o he ool aims o sol e he obs acles abo e
desc ibed by using isual easoning, and specializing he epai
on li le pieces o on ologies ha wi nesses he anomaly (an
anomalous a gumen ).
The idea is based on a p e ious heo e ical analysis o
me eo opological ep esen a ion o ela ionships among he
on ology’s concep s [6], as well as he ounda ional p inciples
o isual on ology cleaning in oduced in [5]. In his way,
he in o ma ion abou concep s appea ing in he a gumen s
is nicely ep esen ed in a clea way. O en, an a gumen
is a e y small po ion o on ology, he e o e, i is easily
ep esen ed and, despi e i s mode a e size, i p o ides a mo e
use ul in o ma ion abou he anomaly han he ull on ology (a
simila a gumen a i e case o debugging is p esen ed in [16]).
Las ly, he ool has o allow (and s ongly induces o) use
in e ac ions on isual ep esen a ion ( he in o ma ion space)
wi h no limi s o classical use analysis in e ac ion, que ying
and na iga ion/b owsing.
The design p inciples desc ibed in his pape ha e been
conside ed in a ool implemen ed as a plug-in o P o ´
eg´
e1. The
ool allows he a angemen o concep s ela ionships because
i implemen s a soundly logical ansla ion o on ology code.
This ea u e is speci ic; o he end-use ools which a e mos ly
based on acili a ing he unde s anding o he on ology (see
e.g. [9], [19]) bu displaying a e y limi ed g aphical ans o -
ma ion o he on ology sou ce. Ano he essen ial ea u e is ha
he epa a ion p ocess has o be model-based, ha is, i has
o exploi he ac he use keep in mind he in ended model
ha he on ology should ep esen , and his model induces
he changes (use only aims o i spa ial model in o eal
one). The e o e, a gumen s epai ing is a ela i ely easy ask,
because i is mo e easible o be ep esen ed han he ull
on ology. Fo mally, he p oblem ha he pape add esses is
desc ibed in [20] as On ology Repai in he ollowing e ms:
1h p://p o ege.s an o d.edu/
Fo an on ology Σ, o any s a emen φ ha is de i able
om Σbu is disco e ed o be inco ec acco ding o he
wo ld, a map πexis s such ha ei he π(φ)is co ec
acco ding o he wo ld and de i able om π(Σ) o , i
his canno be sa is ied, hen π(φ)is no de i able om
π(Σ);
Σ`φ∧ 6|=φ=⇒ ∃π(π(Σ) `π(φ)∧ |=π(φ)∨π(Σ) 6` π(φ))
In such e ms, he ool has o p o ide o he use he
de ini ion o a map πon an a gumen ( he piece o he on ology
used in he p oo o φ).
In o de o implemen he sys em, se e al decisions ha e o
be made.
A. Requi emen s
•The ool con o ms he cogni i e p inciples o isual
on ology cleaning desc ibed in [5] (see sec ion below).
•The me a-on ological in e p e a ion o he concep ual
s uc u e o he on ology [5] is used in bo h di ec ions,
namely om on ology sou ce o spa ial ep esen a ions,
and also when isual a angemen s a e in e p e ed as
logical e isions o on ology code.
•The ool uses wo well-known sys ems, as black-box
modules: P o ´
eg´
e (by using he ool as a new plug-in)
and Race 2(by compu ing me eo opological ela ionships
among concep s).
•The main goal is no he isualiza ion o ull on ologies.
I is designed o isualize ela ions among concep s
implied in an de icien ep esen a ion o he wo ld.
B. S uc u e o he pape
The s uc u e o he pape is as ollows. Nex sec ion is
de o ed o summa ize he main ea u es o he me eo opolog-
ical in e p e a ion o concep ela ionships in an on ology. I
is an ab idged e sion o [5]. Sec ions 3 illus a e s ep by s ep
he wo k low by means o an example. Finally, we conclude
wi h some conclusions o he analysis and a compa ison wi h
simila ools.
II. MEREOTOPOLOGY AND VISUAL COGNITIVE
PRINCIPLES
The spa ial me apho s a e a powe ul ool in human in o -
ma ion p ocessing, al hough he e exis s h ee main obs acles.
Fi s ly, i can be ha d o acili a e he code o he on ology
ha has been epai ed om isual a angemen s. I is he
case o a ool no suppo ed by a o mal seman ics ha , a
he same ime, suppo s such changes. Secondly, he epai -
ing can be, om he poin o iew o compu a ional logic,
complex o be ep esen ed. Finally, isual ep esen a ion o
huge on ologies is an in ica e ask because i is ha d bo h o
comp ehend and o be shown in a sui able way. I makes i s
use app op ia e on ligh -weigh on ologies [10]. The p oblem
is also exace ba ed because logical o malisms ( he basis o
on ology web languages) a e a majo ba ie o end use s’
unde s anding o on ologies, among o he challenges [2]. This
2h p://www. ace -sys ems.com/
ba ie sugges s o add ess he p oblem by ans o ming and
weakening he complexi y o he knowledge ep esen a ion and
easoning (KRR) applied o he sys em, in o de o acili a e
he on ology epai ask o non expe use s.
In his sec ion we b ie ly in oduce he me eo opological
and me aon ological p inciples on which he de elopmen and
design o his ool a e based. We Wo k on he p inciple ha
i we aim o use spa ial easoning echniques o cleaning
on ologies, hen we need o p o ide wi h a heo y on spa ial
en i ies which allows us he ansla ion o he spa ial a ange-
men s o changes on he on ology sou ce. This is he idea
cap u ed by he Main Cogni i e P inciple (MCP) (see [5]) and,
in o de o mee his p inciple, we ha e selec ed a Quali a i e
Spa ial Reasoning (QSR) heo y. In his way, we can also
sa is y he Fi s Cogni i e P inciple (CP1) [5] by ep esen ing
opologically he concep s o he concep ualiza ion associa ed
wi h an on ology by means o non emp y egula egions. No e
ha egula egions comp yse polygons and ci cles.
Due o we a e in e es ed in wo king wi h models o
he on ology which uni e se is a wo-dimensional o h ee-
dimensional space and ha ing in main hose models in e p e
concep symbols as egions, i is clea ha he depic ed knowl-
edge depends on he opological ela ions among egions. The
QSR heo y we ha e chosen is Region Connec ion Calculus
(RCC).
A. The me eo opological heo y RCC
RCC heo y [8], a me eo opological app oach o QSR,
desc ibes opological ea u es o he spa ial ela ions. I has
been use ul in se e al ields o A i icial In elligence such as
Geog aphic In o ma ion Sys ems (GIS) and Spa ial Da abases
[24] [12]. Wi h he help o RCC, CP1 can be sa is ied. I
allows us bo h o eason on spa ial egions and in e change
knowledge be ween on ologies and hei spa ial models. We
conside a g ound ela ion, he connec ion be ween wo e-
gions, which enjoys he e lexi e and symme ical p ope ies.
The meaning o connec ion is: he opological closu es o wo
connec ed egions in e sec . The se o axioms exp essing he
p ope ies and de ini ions o he emaining ela ions (Fig. 1
(le ) con o ms he se o axioms o RCC (see [8]).
On one hand, he se o he eigh bina y ela ions de-
pic ed in Fig. 1 is deno ed by RCC8. These ela ions a e
join ly exhaus i e and pai wise disjoin (JEPD) and RCC8
is ega ded a calculus o Cons ain s Sa is ac ion P oblems
(CSP) [26]. On he o he hand, he e is ano he in e es ing
calculus, RCC5 = {DR, P O, P P, P P i, EQ}. The di e ence
be ween hem is ha while he o me allows us o en ich
he ep esen a ion o knowledge by using on ie s o he
egions, he la e do no . This ac will be discussed abo e.
Al hough i has been empi ically es ablished [17] ha RCC8 is
mo e sui able han RCC5 o he ep esen a ion o opological
ela ions disc imina ed by humans, bo h o hem a e used
he e: RCC5 is app op ia e o sol ing CSPs associa e o a
me eo opological ep esen a ion and RCC8 is use ul o design
a ich ansla ion o a spa ial ep esen a ion o he on ology
code.
Fig. 1. Axioms o RCC ( igh ) and RCC8 spa ial ela ions (le )
B. RCC in e p e ed as a me a-on ology
RCC was he QSR heo y selec ed as o mal suppo o
an on ology cleaning cycle p esen ed a [1], and now, he
use o RCC o ep esen isually he concep s, u ns o
RCC8 in o an on ology on concep ual ela ions. The mos
s aigh o wa d app oach consis s o in e p e ing concep s such
as egions in some model o he heo y. Thus, he s ong
in e p e a ion is de ined wi h he in ended meaning o wo
concep s C1,C2a e connec ed, deno ed by CΣ(C1,C2), i he e
exis s a common elemen in some model o he on ology Σ, i.e.
Σ6|=C1uC2≡ ⊥.
The knowledge we can ep esen by means o he s ong
in e p e a ion o RCC, is limi ed by he ollowing ea u e.
Theo em II.1 [5] The s ong in e p e a ion does no disc im-
ina e he elemen s o RCC8 like on ological ela ions be ween
concep s.
In ac , i C1,C2a e concep s and R∈
{EC, T P P, NT P P, T P P i, NT P P i}, hen ¬RΣ(C1,C2).
I means ha we can no di ec ly conside o RCC8 as
a me aon ology o analysing concep ela ionships in he
s ong in e p e a ion, because such an in e p e a ion can
no ep esen on ie -sensi i e knowledge (i is no able o
dis inguish among TPP and PP, o example). This limi a ion
is sol ed by using o he in e p e a ion p o ided by he
Second Cogni i e P inciple (CP2): The on ie o a spa ial
in e p e a ion o a concep C ep esen s he indi iduals wi h
possible eclassi ica ion C.
The s ong in e p e a ion o he emaining RCC ela ions is
ob ained om hei co esponding de ini ions (Fig. 1). No e
ha he s ong in e p e a ion does no wo k on a conc e e bu
abs ac spa ial in e p e a ion o concep s. By a spa ial model
o an on ology Σis an in e p e a ion Io Σwhose uni e se
is R2(o R3) which in e p e s concep s as egula egions
and such ha CΣ(C1, C2)i and only i I|=C(C1, C2). The
exis ence o an spa ial model is made su e by he heo em:
Theo em II.2 E e y consis en on ology has a spa ial model
P oo : (Ske ch) I an on ology Σis consis en , hen he
cons ain sa is ac ion p oblem (CSP) de ined by he weak
in e p e a ion o RCC- ela ionships [5] among i s concep s is
consis en . Thus, i holds ha he CSP is spa ially consis en
[25], ha is, he e exis s a solu ion in e p e ing concep s as
egula egions
I should be no ed ha Renz’s esul on which is based
abo e heo em only ensu es ha polygonal (no necessa ily
connec ed) egions can be selec ed o in e p e concep s. We
ha e selec ed only uses ec angula egions. Thus he e exis
spa ial con igu a ions ha can no be p ope ly ep esen ed.
Two easons jus i y his decision. On he one hand, i aims
o show use iendly ep esen a ions on ela ions among con-
cep s, and on he o he hand, concep s o ep esen a e hose
in ol ed in a gumen s, which usually deal wi h a ela i ely
small se o concep s.
Once an a gumen is spa ially ep esen ed, in nex sec ion
we analyse how he opological bo de s o egions a e en-
dowed o cogni i e ea u es, by means o RCC8. This ool
in e p e s concep ’s bo de as he se o indi iduals which
migh be candida es o eclassi ica ion.
III. PRAGMATICS IN SPATIAL INTERPRETATION AND
REARRANGEMENT
Based on ounda ional decisions made in abo e sec ion in
his sec ion i desc ibes all he s eps which he ool is based
on.
In o de o exploi RCC8 ea u es by sol ing he limi a ion
abo e commen ed, i in e p e s ECΣ(C1, C2)as ollows:
Σ6|=C1uC2≡⊥ and¬∃C3s. . Σ|=C3 (C1uC2)
Thus, he ela ions {EC, T P P, NT P P, T P P i, NT P P i}
can be e-in e p e ed and i allows us o use RCC8. The
a ionale design is based on h ee laye s (see Fig. 2). They
uses di e en ep esen a ion and easoning sys ems o connec
au oma ed easoning on on ologies wi h spa ial easoning. This
connec ion mus be showed o he end use by means o a
g aphical in e ace whe e spa ial ep esen a ion o me eo opo-
logical ela ions is displayed.
The (Fig. 2) wo k low s a s wi h a spa ial ep esen a ion o
he RCC ela ionships among concep s o a se . I is done by
using an au oma ed easoning sys em o compu e hese ela-
ions. In ac , his key s ep consis s in a ansla ion om logical
in o ma ion on concep ualiza ion o a CSP on spa ial ela ions.
By sol ing his CSP, a spa ial encoding o concep ualiza ions
is ob ained and g aphically ep esen ed o use eedback. The
solu ion is isualized. I he use conside s ha he e exis
Fig. 2. Repai ing Wo k low
an anomaly (i ep esen s an anomalous ep esen a ion o he
wo ld, i is usually a subse o concep s o which on ology
s a es a ela ionship which is no ue in he wo ld), hen i
p o ides an in e ace o spa ially ea ange he ep esen a ion.
Nex , i ansla es he new spa ial con igu a ion o on ology
sou ce code.
IV. AN EXAMPLE
To illus a e he ull edi ing p ocess we ha e chosen a well-
known on ology, he Ins uc ional Objec s3on ology, which
can be ound a SchemaWeb4
Fig. 3. Classes hie a chy iew in P o ´
eg´
e and classes selec ion
A. A gumen s
The i s s ep o he p ocess o epai he on ology, is
o selec he a gumen s om he on ology o s udy up on.
Pa icula ly, his on ology has no indi iduals, i jus has
classes, hence we only need he Classes Lis o selec he
a gumen s.
This example looks in e es ing when we s udy he “Exam-
ple” and “Coun e Example” classes. They bea an o e lapping
3h p://www.ac i ema h.o g/˜ cull ich/oio/Ins uc ionalObjec s.owl
4h p://www.schemaweb.in o/
ela ionship be ween hemsel es, which means ha i could ex-
is s some indi iduals o classes which belong o he in e sec ion
o hem. Suppose, o example, ha ou use hinks ha i is
no possible in his men al s a e (he aims o apply he on ology
in a conc e e kind o p oblems) and, he e o e, he de e mines
ha he ela ion among hese classes has o be he disjoin one
(DC).
Fig. 3 shows how he use selec s needed a gumen s om
he classes lis . He selec s “Example”, “Coun e Example” and
some o he ones ela ed o hem in o de o imp o e he
easoning p ocess.
B. G aphical ep esen a ion
As i is explained abo e, all he ela ions among a gumen s,
in RCC5, a e compu ed and op imized o be sen o he CSP.
F om his ask, we ob ain he coo dina es belonging o he
egula egions and his ac ion le us o build he g aphical
ep esen a ion o all he ela ions.
Fig. 4. Ini ial g aphical ep esen a ion
C. Mo emen s
Once ep esen ed he selec ed concep s (see Fig. 4) no e ha
he e a e some ela ions which a e no co ec , in spi e o being
consis en . In ou example, “Example” and “Coun e Example”
classes ha e o be disjoin ed, which i means ha we ha e
o esize “Ilus a ion” class and mo e “Example” class up o
make i disconnec ed o “Coun e Example”. We ealize all he
possible mo emen s in plug-in, and we u n an o e lapping
in o a disjoin ela ion (see Fig. 5).
Fig. 5. Resizing (le ) and ansla ion ( igh )
These mo emen s could inse anomalies in o he on ology,
essen ially on classes and indi iduals which a e no g aphically
ep esen ed. This kind o anomalies is sol ed by assuming
some c i e ia as de aul and, i he epai ing is no easible, a
wa ning message is displayed and all classes and indi iduals
which a e in ol ed in he anomaly a e included.
D. Sa ing and inal esul
When all he mo emen s a e pe o med and he men al use
s a es he is acco ding o he on ology, we can p oceed o sa e
pe manen ly all he changes in ou knowledge da abase o
on ology.
In addi ion, a his s age is when, i he use has inse ed
some inconsis ence in o he on ology, i has o be de ec ed and
decisions o a oid i ha e o be made. The ool has o apply
some se o c i e ia as de aul which helps he use o make
hese decisions, i he has no a clea answe . These c i e ia a e
always based on he in en ion o modi y knowledge base as
less as possible.
In ou example, i could exis a class o indi idual which
belongs o “Example” and “Coun e Example” classes simul-
aneously, and he e o e, when hey u ns in o disjoin , he
use is inse ing an inconsis ency. I could ix his si ua ion in
wo ways: On one hand, i he classes ha e been ep esen ed,
when hey a e mo ed he use has speci ied, explici ly, he new
ela ion be ween he classes which in oduce he inconsis ence,
and hence i disappea s. On he o he hand, i he e exis s a
class a ec ed and i is no ep esen ed, i conside s ha he
a ec ed class belongs o he class which was no mo ed.
Fig. 6. Upda ing on ology sou ce
As he las mo emen in ol ed in ou example, we
ha e made he change P O(Example, Coun e Example)⇒
DC(Example, Coun e Example)in he on ology, and ob-
ained he changes in axioms (see Fig. 6 down, om P o ´
eg´
e
in e ace).
Along his p ocess, he use has ob ained a modi ica ion o
his on ology wi hou needing expe knowledge on on ological
enginee ing.
V. CLOSING REMARKS AND RELATED WORK
In his pape an in elligen ool o on ology epai designed
o non-expe s on on ology enginee ing is p esen ed. The
a ionale behind he ool is ha logical ela ionships among
concep s can be spa ially ep esen ed, as well as he changes in
he ep esen a ion can be ansla ed o on ology code. RCC8-
based spa ial encoding p o ides us wi h a o mal seman ics
whe e spa ial a angemen s mean on ology e ision. The en-
coding es ablishes a co espondence be ween he concep ual-
iza ion implici in he On ology and a ealm well known o he
use . We desc ibed se e al spa ial encodings based on di e en
me eo opological in e p e a ions o on ologies.
Fu he mo e, we exploi logical ea u es o RCC o analyze
he impac o e ision on he on ology i sel . I is wo h o
no e ha he ool can be eused o o he ela ed p oblems
as o example on ology alignmen , and he analysis o he
ela ions among concep s in di e en e sions o an on ology.
Pa icula ly in e es ing is he case o analyzing he di e ence
be ween wo DL on ologies, whe e he spa ial ep esen a ion
o concep s (and anonymous classes) o bo h on ologies can
acili a e he wo k o on ology enginee s [11].
The idea o combining spa ial calculi wi h Desc ip ion
Logics is a esea ch line bo h in he Seman ic Web and also in
he Desc ip ion Logics communi y (see e.g. [13], [23]). The
app oach p esen ed does no a emp o combine bo h heo ies,
jus use a ansla ion o DL o QSR o acili a e use in e ac ion
by isual easoning. This app oach was success ul in p e ious
case s udies [4].
A g ea numbe o ools o on ologies ha suppo s isual
ep esen a ion exis s, e en also suppo ing a a ie y o asks
such as da a analysis and que ies [9], [10]. Fo example,
An a i.ca’s Visual Ne 5o AquaB owse display on ology
sou ces as maps o g aphs, and que ies can be made bu
hey canno be upda ed. They also ha e p oblems o display
indi iduals and in e sec ions. Howe e hese wo ks a e mos ly
ocused on isual ep esen a ion and hey lack bo h in e ence
mechanisms and o mal seman ics ep esen a ions ou lined
he e ope a es beyond jus p ima ily mapping he on ology
in o ma ion/concep ualiza ion s uc u e. A la ge numbe o
ools a e based on G aphViz6and hey ha e a nice isual ep-
esen a ion wi hou p o iding ools o changing he on ology.
O he example is Jambalaya, a plug-in c ea ed o P o ´
eg´
e
which uses Sh imp o isualize he knowledge bases ha he
use has c ea ed7. As abo e ools, Jambalaya does no p o ide
spa ial ea angemen s o epai he on ology. O he ool which
add esses he p oblem o use ’s comp ehension o he s uc u e
o he on ology is KC-Viz [21] which p o ides a ele an
isualiza ion o he on ology, acili a ing he na iga ion and
b owsing.
I is app op ia e o indica e ha he anomalies could be
o igina ed om o he di e en easons, hey no only come
om he concep ualiza ion. Roles (objec p ope ies) a e also
an impo an sou ce o anomalies. We will be ocused on
me eo opological encodings o hem, and de elop a ool ha
can assis o use s o epai he anomalies coming om oles.
Finally, no e ha we use small on ologies pieces because
ou epa a ion me hod is a gumen a i e and i does no need
5h p://www.an a c i.ca
6h p://www.g aph iz.o g
7h p://www. hechiselg oup.o g/jambalaya

he whole on ology. Fo medium and la ge size on ologies,
isual ep esen a ion could be unmanageable, howe e i could
be in e es ing o adap he spa ial seman ics o wo k wi h
o he isual encodings as he hype bolic plane [18]. F om he
poin o iew o Mul iagen Sys ems, On ology Repai Rys-
em (ORS)[20] was de eloped o epai on ology misma ches
be ween agen s wi h simila on ologies in a mul iagen sys em
(MAS) en i onmen see also [15]. Cu en ly he design p inci-
ples p o ide assis ance o sol ing he misma ches o humans.
Howe e , we ha e de eloped au oma ed seman ic nego ia ion
me hods [3] which can en ich he me hod in he u u e.
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