Motivation DL-program: rules P + consistent ontology O DL-atom 1 - PowerPoint PPT Presentation

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Computing Repairs for Inconsistent DL-programs over EL Ontologies Thomas Eiter Michael Fink Daria Stepanova Knowledge-Based Systems Group, Institute of Information Systems, Vienna University of Technology http://www.kr.tuwien.ac.at/ JELIA 2014–September, 26, 2014 1 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Motivation • DL-program: rules P + consistent ontology O DL-atom 1 (loose coupling combination approach) • DL-atoms serve as query interfaces to O P O • Possibility to add info from P to O prior to DL-atom 2 querying it: bidirectional data flow 1 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Motivation • DL-program: rules P + consistent ontology O DL-atom 1 (loose coupling combination approach) • DL-atoms serve as query interfaces to O P O • Possibility to add info from P to O prior to DL-atom 2 querying it: bidirectional data flow However, information exchange between P and O can cause inconsistency of the DL-program (absence of answer sets). 1 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Motivation • DL-program: rules P + consistent ontology O DL-atom 1 (loose coupling combination approach) • DL-atoms serve as query interfaces to O P O • Possibility to add info from P to O prior to DL-atom 2 querying it: bidirectional data flow However, information exchange between P and O can cause inconsistency of the DL-program (absence of answer sets). Repair answer sets [E et al, IJCAI 2013] Algorithm based on complete support families [E et al, ECAI 2014] Effective for DL - Lite A (few small support sets per DL-atom) Not well suited for EL (might be many / large support sets . . . ) In this work: algorithm for repairing DL-programs over EL ontologies 1 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Overview Motivation DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion 2 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion EL Description Logic • Lightweight DL, widely used in biology, medicine and other domains • Concepts and roles model sets of objects and their relationships • EL -concept is formed according to the rule C ::= A | ⊤ | C ⊓ C | ∃ R . C • An EL ontology O = �T , A� consists of • TBox T specifying inclusions/equivalence between EL -concepts C ⊑ D C ≡ D • ABox A specifying facts that hold in the domain A ( b ) R ( a , b ) Example � � Blacklisted ⊑ Staff T = BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubject . Blacklisted � Blacklisted ( john ) � A = StaffRequest ( r1 ) hasSubject ( r1 , john ) 3 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion EL Description Logic • Lightweight DL, widely used in biology, medicine and other domains • Concepts and roles model sets of objects and their relationships • EL -concept is formed according to the rule C ::= A | ⊤ | C ⊓ C | ∃ R . C • An EL ontology O = �T , A� consists of • TBox T specifying inclusions/equivalence between EL -concepts C ⊑ D C ≡ D • ABox A specifying facts that hold in the domain A ( b ) R ( a , b ) • Normalized TBox T norm contains only inclusions of the form A 1 ⊑ R . A 21 A 1 ⊑ A 2 A 1 ⊓ A 2 ⊑ A 3 ∃ R . A 1 ⊑ A 2 1 A i is an atomic concept 3 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Example: DL-program Π = �O , P� is a DL-program   (1) Blacklisted ⊑ Staff     (2) StaffRequest ≡ ∃ hasAct . Actqcap ∃ hasSubj . Staff ⊓ ∃ hasTarg . Proj   O = (3) BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubj . Blacklisted       (4) StaffRequest ( r1 ) (5) hasSubj ( r1 , john ) (6) Blacklisted ( john )   (7) projfile ( p1 ); ( 8 ) hasowner ( p1 , john );   P = (9) grant ( r1 ) ← DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) , not deny ( r1 )   (10) deny ( r1 ) ← DL [; BLStaffRequest ]( r1 ) 4 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Example: DL-program Π = �O , P� is a DL-program   (1) Blacklisted ⊑ Staff     (2) StaffRequest ≡ ∃ hasAct . Actqcap ∃ hasSubj . Staff ⊓ ∃ hasTarg . Proj   O = (3) BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubj . Blacklisted       (4) StaffRequest ( r1 ) (5) hasSubj ( r1 , john ) (6) Blacklisted ( john )   (7) projfile ( p1 ); ( 8 ) hasowner ( p1 , john );   P = (9) grant ( r1 ) ← DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) , not deny ( r1 )   (10) deny ( r1 ) ← DL [; BLStaffRequest ]( r1 ) • Interpretation: I = { projfile ( p1 ) , hasowner ( p1 , john ) , deny ( r1 ) } = O projfile ( p1 ) ; • Satisfaction relation: I | = O DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) I | = O DL [; BLStaffRequest ]( r1 ) I | • Semantics: in terms of answer sets, i.e. founded models (weak, flp, . . . ) • I is a weak and flp answer set 4 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Example: DL-program Π = �O , P� is a DL-program   (1) Blacklisted ⊑ Staff     (2) StaffRequest ≡ ∃ hasAct . Actqcap ∃ hasSubj . Staff ⊓ ∃ hasTarg . Proj   O = (3) BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubj . Blacklisted       (4) StaffRequest ( r1 ) (5) hasSubj ( r1 , john ) (6) Blacklisted ( john )   (7) projfile ( p1 ); ( 8 ) hasowner ( p1 , john );   P = (9) grant ( r1 ) ← DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) , not deny ( r1 )   (10) deny ( r1 ) ← DL [; BLStaffRequest ]( r1 ) • Interpretation: I = { projfile ( p1 ) , hasowner ( p1 , john ) , deny ( r1 ) } = O projfile ( p1 ) ; • Satisfaction relation: I | = O DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) I | = O DL [; BLStaffRequest ]( r1 ) I | • Semantics: in terms of answer sets, i.e. founded models (weak, flp, . . . ) • I is a weak and flp answer set 4 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Example: DL-program Π = �O , P� is a DL-program   (1) Blacklisted ⊑ Staff     (2) StaffRequest ≡ ∃ hasAct . Actqcap ∃ hasSubj . Staff ⊓ ∃ hasTarg . Proj   O = (3) BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubj . Blacklisted       (4) StaffRequest ( r1 ) (5) hasSubj ( r1 , john ) (6) Blacklisted ( john )   (7) projfile ( p1 ); ( 8 ) hasowner ( p1 , john );   P = (9) grant ( r1 ) ← DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) , not deny ( r1 )   (10) deny ( r1 ) ← DL [; BLStaffRequest ]( r1 ) • Interpretation: I = { projfile ( p1 ) , hasowner ( p1 , john ) , deny ( r1 ) } = O projfile ( p1 ) ; • Satisfaction relation: I | = O DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) I | = O DL [; BLStaffRequest ]( r1 ) I | • Semantics: in terms of answer sets, i.e. founded models (weak, flp, . . . ) • I is a weak and flp answer set 4 / 13

Motivation Overview DL-programs Support Sets for DL-atoms Repair Answer Set Computation over EL Experiments Conclusion Example: DL-program Π = �O , P� is a DL-program   (1) Blacklisted ⊑ Staff     (2) StaffRequest ≡ ∃ hasAct . Actqcap ∃ hasSubj . Staff ⊓ ∃ hasTarg . Proj   O = (3) BLStaffRequest ≡ StaffRequest ⊓ ∃ hasSubj . Blacklisted       (4) StaffRequest ( r1 ) (5) hasSubj ( r1 , john ) (6) Blacklisted ( john )   (7) projfile ( p1 ); ( 8 ) hasowner ( p1 , john );   P = (9) grant ( r1 ) ← DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) , not deny ( r1 )   (10) deny ( r1 ) ← DL [; BLStaffRequest ]( r1 ) • Interpretation: I = { projfile ( p1 ) , hasowner ( p1 , john ) , deny ( r1 ) } = O projfile ( p1 ) ; • Satisfaction relation: I | = O DL [ Proj ⊎ projfile ; StaffRequest ]( r 1 ) I | = O DL [; BLStaffRequest ]( r1 ) I | • Semantics: in terms of answer sets, i.e. founded models (weak, flp, . . . ) • I is a weak and flp answer set 4 / 13