Data Repair of Inconsistent DL-Programs Thomas Eiter Michael Fink - PowerPoint PPT Presentation

Motivation Overview DL-programs Repair answer sets Computation Conclusion Data Repair of Inconsistent DL-Programs Thomas Eiter Michael Fink Daria Stepanova Knowledge-Based Systems Group, Institute of Information Systems, Vienna University of Technology http://www.kr.tuwien.ac.at/ IJCAI 2013 –August 6, 2013 1 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Motivation • DL-program: ontology + rules (loose coupling combination approach); • DL-atoms serve as query interfaces to ontology; • Possibility to add information from the rule part to ontology prior to querying it allows for bidirectional information flow. However, information exchange between rules and ontology can have unforeseen effects and cause inconsistency of the DL-program (absence of answer sets). 1 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Motivation • DL-program: ontology + rules (loose coupling combination approach); • DL-atoms serve as query interfaces to ontology; • Possibility to add information from the rule part to ontology prior to querying it allows for bidirectional information flow. However, information exchange between rules and ontology can have unforeseen effects and cause inconsistency of the DL-program (absence of answer sets). In this work: Repair data part of the ontology ( DL - Lite A ), i.e. change ontology ABox s.t. the resulting DL-program is consistent. 1 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Overview Motivation DL-programs Repair answer sets Computation Conclusion 2 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion DL - Lite A • Lightweight Description Logic for accessing large data sources. • Concepts and roles model sets of objects and their relationships. R → P | P − C → A | ∃ R • A DL - Lite A ontology O = �T , A� consists of: • TBox T specifying constraints at the conceptual level. C 1 ⊑ C 2 , C 1 ⊑ ¬ C 2 , R 1 ⊑ R 2 , R 1 ⊑ ¬ R 2 , ( funct R ) . • ABox A specifying the facts that hold in the domain. A ( b ) P ( a , b ) 3 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion DL - Lite A • Lightweight Description Logic for accessing large data sources. • Concepts and roles model sets of objects and their relationships. R → P | P − C → A | ∃ R • A DL - Lite A ontology O = �T , A� consists of: • TBox T specifying constraints at the conceptual level. C 1 ⊑ C 2 , C 1 ⊑ ¬ C 2 , R 1 ⊑ R 2 , R 1 ⊑ ¬ R 2 , ( funct R ) . • ABox A specifying the facts that hold in the domain. A ( b ) P ( a , b ) Example � � � � Child ⊑ ∃ hasParent hasParent ( john , pat ) T = A = Female ⊑ ¬ Male Male ( john ) 3 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion DL - Lite A • Lightweight Description Logic for accessing large data sources. • Concepts and roles model sets of objects and their relationships. R → P | P − C → A | ∃ R • A DL - Lite A ontology O = �T , A� consists of: • TBox T specifying constraints at the conceptual level. C 1 ⊑ C 2 , C 1 ⊑ ¬ C 2 , R 1 ⊑ R 2 , R 1 ⊑ ¬ R 2 , ( funct R ) . • ABox A specifying the facts that hold in the domain. A ( b ) P ( a , b ) Example � � � � Child ⊑ ∃ hasParent hasParent ( john , pat ) T = A = Female ⊑ ¬ Male Male ( john ) Conjunctive query answering in DL - Lite A is tractable [Calvanese et al. , 2007]. 3 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: DL-program Π = �O , P � is a DL-program. � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat ) 4 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: DL-program Π = �O , P � is a DL-program. � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );   P = (9) hasfather ( john , pat ) ← DL [ Male ⊎ boy ; Male ]( pat ) ,   DL [; hasParent ]( john , pat ) • interpretation: I = { ischildof ( john , alex ) , boy ( john ) , hasfather ( john , pat ) } ; = O boy ( john ) ; I | = O DL [; hasParent ]( john , pat ) ; • satisfaction relation: I | • semantics is given in terms of answer sets, which are x -founded models; • flp and weak semantics are relevant in this work; • I is both weak - and flp -founded model. 4 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) 5 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) 5 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) 5 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � is inconsistent! � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) No answer sets. 5 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � is consistent! � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Male ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) I 1 = { ischildof ( john , alex ) , boy ( john ) } 5 / 18

Motivation Overview DL-programs Repair answer sets Computation Conclusion Example: Inconsistent DL-program Π = �O , P � is consistent! � ( 1 ) Child ⊑ ∃ hasParent ( 4 ) Female ( pat ) � O = ( 2 ) Adopted ⊑ Child ( 5 ) Male ( john ) ( 3 ) Female ⊑ ¬ Male ( 6 ) hasParent ( john , pat )   (7) ischildof ( john , alex ); ( 8 ) boy ( john );       (9) hasfather ( john , pat ) ← DL [; Male ⊎ boy ; Male ]( pat ) ,       DL [; hasParent ]( john , pat ); P = (10) ⊥ ← not DL [; Adopted ]( john ) , pat � = alex ,       hasfather ( john , pat ) , ischildof ( john , alex ) ,       not DL [ Child ⊎ boy ; ¬ Male ]( alex ) I 1 = { ischildof ( john , alex ) , boy ( john ) } 5 / 18