Local tableaux for reasoning in distributed description logics a - - PowerPoint PPT Presentation
DDL reasoning L. Serafini & A. Tamilinr Local tableaux for reasoning in distributed description logics a Luciano Serafini 1 and Andrei Tamilin 2 1 IRST, Trento, Italy 2 University of Trento, Italy DL workshop 2004 a Alex Borgida, and
DDL reasoning
Luciano Serafini1 and Andrei Tamilin2
1IRST, Trento, Italy 2University of Trento, Italy
DL workshop 2004
aAlex Borgida, and PELLET’s Team
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DDL reasoning
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DDL reasoning
GOAL Support Distributed Reason- ing in a web of ontologies REQUIREMENTS
tologies
tools
tologies
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DDL reasoning
Temporarily enrich Word-Net plain list of jobs with the ISCO-88 standard classification for professions.
ISCO-88 Wordnet 2 Professionals 21 Physical, mathematical and engineering science profess. 211 Physicists, chemists and related professionals . . . 214 Architects, engineers and related professionals 2141 Architects, town and traffic planners 2146 Chemical engineers 3 Technicians and associate professionals 31 Physical and engineering science associate professionals 311 Physical and engineering science technicians 3111 Chemical and physical science technicians 3112 Civil engineering technicians 312 Computer associate professionals adEntity Causal agency Cause Causal agent . . . Person Self Nurser Engineer Capitalist Worker Captor Commoner
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DDL reasoning
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DDL reasoning
Use some (semi)automatic matching procedure (not our foucs here)
Distributed Description Logics (DDL)
Distributed Tableaux Reasoning in DDL
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DDL reasoning
Given a set I of indexes.
i : x
j : y
(into bridge rules)
i : x
✄ ✁ ✂j : y
(onto bridge rules) where x and y are concepts/role/individuals of DL i and DL j.
Ti
✝i
✞I
✟✡✠ ☛where
– Ti is a T-box of DLi; –
✠is a set of bridge rules in DDL
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DDL reasoning
ISCO : Professionals
WNP : Worker ISCO : Architects Engineers and Relate Profess.
✄ ✁ ✂WNP : Engineer
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DDL reasoning
ISCO :
WNP :
✁Child
ISCO : Doorkeepers watchpersons and. . .
✄ ✁ ✂WNP : Gatekeeper
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DDL reasoning
A distributed interpretation for a distributed T-box
I i
✝i
✞I
✟ ✆rij
✝i
✆✞✝j
✞I
✟consisting of
j
✠I i.e., a binary relation rij
✡∆I i
☛∆I j.
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DDL reasoning
We have to give a distributed interpretation of a set of T-boxes, where some of them are
Distributed T-Bos
☎T1
✟T2
✟T3
✟T4
✟T5
☛Distributed interpretation
☎I 1
✟I 2
✟I 3
✟I 4
✟I 5
☛I 2
✟I 4
✟I 5 are interpretations of T2
✟T4
✟T5, respectively I 1 and I 3 are Paritally inconsistent local interpretation is an interpretation where
be interpreted in a non empty set.
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DDL reasoning
d i : A
j : G,
if
rij
✁AI i
✂ ✡GI j;
r
12
r
12(A)
A dom1 dom 2 G DL 2004 – June 8, 2004 12
DDL reasoning
d i : B
✄ ✁ ✂j : H,
if
rij
✁BI i
✂r
12
r
12(B)
dom1 dom 2 B H DL 2004 – June 8, 2004 13
DDL reasoning
Isa Isa Worker Engineer Professionalse ISCO 88 WordNet
Architects_Engineers_ and related professional
ISCO : Professionals
WNP : Worker ISCO : Architects Engineers and Relate Profess.
✄ ✁ ✂WNP : Engineer
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DDL reasoning
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DDL reasoning
T1
A
Bn, (Local Subsumption) 1 : A
✄ ✁ ✂2 : G 1 : B1
2 : H1
. . .
1 : Bn
2 : Hn
✄ ☎ ☎ ☎ ☎ ☎ ☎ ✆ ☎ ☎ ☎ ☎ ☎ ☎ ✝(Bridge rules in
✠12)
d 2 : G
Bn
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DDL reasoning
T1
✟T2
✟✡✠12
☛be a distributed T-box,
X
T2
✂ ✠12
✁T1
✂X
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DDL reasoning
12
We propose a tableaux based distributed algorithm, build on top of local reasoner for each
DLi.
Tabi
✁Φ
✂computes a finite representation of a DLi-tableaux for Φ in Ti
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DDL reasoning
dTab j
1: T=Tab j
;
✂perform local reasoning and create completion tree
✄2: if (T is not clashed) then 3:
for each open branch β in T and each node x of β do
4: A
☎ ✆A
✝i : A
✞ ✟ ✠j : G
✡G
☛L
;
5: B
☎ ✆B
✝i : B
✌ ✟ ✠j : H
✡ ✍H
☛L
;
6:
if A
✎ ☎/ 0 and B
✎ ☎/ 0 then 7:
for each A
☛A do 8:
if (dTabi
B
✁is not satisfiable) then
9:
close β;
✂clash in x
✄10:
break;
✂verify next branch
✄11:
end if
12:
end for
✂All bridge rules involving x are applied
✄13:
end if
14:
end for
✂all branches are verified
✄15: end if 16: if (T is clashed) then 17:
return unsatisfiable;
18: else 19:
return satisfiable;
20: end if 21: END
T1
✒✔✓A
✕B1
✖ ✗ ✗ ✗ ✖Bn, 1 : A
✘ ✙ ✚2 : G 1 : B1
✛ ✙ ✚2 : H1
. . .
1 : Bn
✛ ✙ ✚2 : Hn
✜12
✒✔✓d 2 : G
✕2 : H1
✖ ✗ ✗ ✗ ✖Bn
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DDL reasoning
manager Peer ontology manager Peer ontology Peer ontology manager
communication)
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DDL reasoning
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DDL reasoning
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DDL reasoning
ε-connection DDL is a special case of ε-connection. Some difference in the representation
Logic of context DDL is clearly related with both Mc Carthy’s and Giunchiglia’s logics of
contexts
DL for information integration Catarci & Lenzerini CIS. C-OWL language proposal DDL provide a formal semantics and reasoning support for for
C-OWL.
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DDL reasoning
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DDL reasoning
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