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 PELLET’s Team DL 2004 – June 8, 2004 1
DDL reasoning L. Serafini & A. Tamilinr Talk Overview 1. Motivations 2. Distributed description logics (DDL) 3. Basic logical properties 4. Checking subsuption in DDL 5. Conclusion DL 2004 – June 8, 2004 2
DDL reasoning L. Serafini & A. Tamilinr Motivation GOAL Support Distributed Reason- ing in a web of ontologies REQUIREMENTS 1. minimal changes on the on- tologies 2. Reuse previous theory and tools 3. Deal with heterogenaous on- tologies DL 2004 – June 8, 2004 3
DDL reasoning L. Serafini & A. Tamilinr Example Temporarily enrich Word-Net plain list of jobs with the ISCO-88 standard classification for professions. ISCO-88 Wordnet 2 Professionals adEntity 21 Physical, mathematical and engineering science profess. Causal agency 211 Physicists, chemists and related professionals Cause . Causal agent . . . . 214 Architects, engineers and related professionals . 2141 Architects, town and traffic planners Person 2146 Chemical engineers Self 3 Technicians and associate professionals Nurser 31 Physical and engineering science associate professionals Engineer 311 Physical and engineering science technicians Capitalist 3111 Chemical and physical science technicians Worker 3112 Civil engineering technicians Captor 312 Computer associate professionals Commoner DL 2004 – June 8, 2004 4
DDL reasoning L. Serafini & A. Tamilinr Proposed Solution 1. Discover mappings between ISCO-OO, and (subpart of) WorNet 2. Represent ISCO-88, Word-Net, and Mappings in a logical formalism ; 3. Define and implement a suitable decision procedure DL 2004 – June 8, 2004 5
DDL reasoning L. Serafini & A. Tamilinr Proposed Solution 1. Discover mappings between ISCO-OO, and (subpart of) WorNet Use some (semi)automatic matching procedure (not our foucs here) 2. Represent ISCO-88, Word-Net, and Mappings in a logical formalism ; Distributed Description Logics (DDL) 3. Define and implement a suitable decision procedure Distributed Tableaux Reasoning in DDL DL 2004 – June 8, 2004 6
✝ ✞ ☛ ✆ ☎ ✠ ✂ � ✁ ✂ ✁ ✄ DDL reasoning L. Serafini & A. Tamilinr DDL: Syntax Given a set I of indexes. • A DDL is a family of description logics DL i one for each i . • A Bridge Rule from i to j , in a DDL is an expression of the following forms: 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 . • a Distributed T-box is a pair T i where i I ✟✡✠ – T i is a T-box of DL i ; – is a set of bridge rules in DDL DL 2004 – June 8, 2004 7
� ✁ ✂ ✄ ✁ ✂ DDL reasoning L. Serafini & A. Tamilinr Bridge Rules: Example - 1/2 ISCO : Professionals WNP : Worker ISCO : Architects Engineers and Relate Profess. WNP : Engineer DL 2004 – June 8, 2004 8
✁ ✄ ✂ ✁ � � ✁ ✂ DDL reasoning L. Serafini & A. Tamilinr Bridge Rules: Example - 2/2 ISCO : WNP : Child ISCO : Doorkeepers watchpersons and. . . WNP : Gatekeeper DL 2004 – June 8, 2004 9
✟ ✟ ✞ ✠ � ✡ ☛ ☎ ✆ ✝ ✝ ✟ ✞ ✆ DDL reasoning L. Serafini & A. Tamilinr DDL: Semantics A distributed interpretation for a distributed T-box is a pair I i r ij i I i j I ✁✄✂ ✆✞✝ consisting of • a local interpretation I i for DL i over domain ∆ I i , and ∆ I i ∆ I j . • a domain relation from i to j , for each i j I i.e., a binary relation r ij DL 2004 – June 8, 2004 10
✟ ☛ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ☎ ✟ ☎ ✟ ✟ ✟ � ☛ DDL reasoning L. Serafini & A. Tamilinr Local interpretation We have to give a distributed interpretation of a set of T-boxes, where some of them are inconsistent. (Consistent, Inonsistent) T 1 T 2 T 3 T 4 T 5 Distributed T-Bos I 1 I 2 I 3 I 4 I 5 Distributed interpretation I 2 I 4 I 5 are interpretations of T 2 T 4 T 5 , respectively I 1 and I 3 are Paritally inconsistent local interpretation is an interpretation where can be interpreted in a non empty set. DL 2004 – June 8, 2004 11
✂ ✁ � ✂ � ✁ ✂ ✡ ✁ DDL reasoning L. Serafini & A. Tamilinr Bridge rules: Satisfi ability (into) d i : A j : G , if A I i G I j ; r ij r 12 A r 12 (A) G dom 2 dom 1 DL 2004 – June 8, 2004 12
✂ ✁ � ✂ ✄ ✁ ✂ � ✁ DDL reasoning L. Serafini & A. Tamilinr Bridge rules: Satisfi ability (onto) d i : B j : H , if B I i H I j ; r ij r 12 B H r 12 (B) dom 2 dom 1 DL 2004 – June 8, 2004 13
✁ ✄ ✂ ✂ ✁ � DDL reasoning L. Serafini & A. Tamilinr DDL: Subsumption propagation Professionalse Worker Isa Isa Architects_Engineers_ Engineer and related professional ISCO 88 WordNet ISCO : Professionals WNP : Worker ISCO : Architects Engineers and Relate Profess. WNP : Engineer DL 2004 – June 8, 2004 14
DDL reasoning L. Serafini & A. Tamilinr Reasoning in DDL DL 2004 – June 8, 2004 15
✄ ✂ � ✠ ✝ ☎ ☎ � ✁ ☎ ✁ ☎ ☎ ☎ ☎ ☎ ☎ ☎ ✆ ✂ � ☎ ✂ ✁ ✂ � ✂ ✂ � ✂ ✁ ✂ � ✂ ✁ ✁ � ✄ ✁ ✂ ✂ ☎ DDL reasoning L. Serafini & A. Tamilinr Generalized Subsumption propoagation T 1 A B 1 B n , (Local Subsumption) 1 : A 2 : G 1 : B 1 2 : H 1 (Bridge rules in 12 ) . . . 1 : B n 2 : H n d 2 : G 2 : H 1 B n 12 DL 2004 – June 8, 2004 16
✂ � ✁ ✂ ✠ ✂ �✁ � ✂ � � � ☛ ✟ � ✂ ☎ DDL reasoning L. Serafini & A. Tamilinr Completeness of Generalized Subsumption propoagation T 1 T 2 be a distributed T-box, 12 12 ✟✡✠ Y : 2 T 2 T 1 X X Y 12 12 DL 2004 – June 8, 2004 17
✁ ✂ DDL reasoning L. Serafini & A. Tamilinr Checking subsumption itn 12 We propose a tableaux based distributed algorithm, build on top of local reasoner for each DL i . Φ Tab i computes a finite representation of a DL i -tableaux for Φ in T i DL 2004 – June 8, 2004 18
✗ ✏ ✗ ✂ ✗ ✗ ✖ ✁ ✑ ✍ � ✖ ☛ ☎ ✎ ✗ ✎ ☞ ✁ � ☛ ✄ ✕ ✡ ✛ ✖ ✕ ✗ ✖ ✘ ✙ ✚ ✄ ✂ ✂ ✙ ✚ ✄ ✂ ✛ ✙ ✚ ✄ ✜ ✍ ☎ ✠ ✆ � ☛ ✡ ✟ ✞ ✝ ☎ ☞ ✄ ✂ ✁ � ✁ � ✁ ✠ ✌ ✆ ☎ ✝ ✟ DDL reasoning L. Serafini & A. Tamilinr Φ dTab j Φ 1: T = Tab j ; perform local reasoning and create completion tree 2: if ( T is not clashed) then T 1 A B 1 B n , for each open branch β in T and each node x of β do ✒✔✓ 3: 1 : A 2 : G 4: A A i : A j : G G L x ; 5: 1 : B 1 2 : H 1 B B i : B j : H H L x ; 0 and B / 0 then / 6: if A . . 7: . for each A A do 8: if ( dTab i A B is not satisfiable) then 1 : B n 2 : H n close β ; 9: clash in x d 2 : G 2 : H 1 B n 10: break; verify next branch 12 ✒✔✓ 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 DL 2004 – June 8, 2004 19
DDL reasoning L. Serafini & A. Tamilinr Implementation Peer ontology Peer ontology manager manager Peer ontology manager • Peer-to-peer architecture (communication based on standard HTTP based communication) • Ontology manager based on PROTEGE • Local reasoner Tab i based on PELLET DL 2004 – June 8, 2004 20
DDL reasoning L. Serafini & A. Tamilinr DL 2004 – June 8, 2004 21
DDL reasoning L. Serafini & A. Tamilinr DL 2004 – June 8, 2004 22
DDL reasoning L. Serafini & A. Tamilinr Related work ε -connection DDL is a special case of ε -connection. Some difference in the representation of local inconistency 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. DL 2004 – June 8, 2004 23
DDL reasoning L. Serafini & A. Tamilinr Conclusion • DDL formal semantics for distributed partially inconsistent and Heterogeneous ontologies • Theoretical characterization of subsumption in DDL with atomic bridge rules • Sound and complete algorithm computing subsumption in DDL • Prototype implementation based on PELLET DL 2004 – June 8, 2004 24
DDL reasoning L. Serafini & A. Tamilinr GRAZIE! DL 2004 – June 8, 2004 25
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