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Explanations for
DL-Lite
Alexander Borgida 2
Diego Calvanese 1
Mariano Rodríguez-Muro 1
1
1 Free University of Bozen Bolza...
Outline
• Explanations
• DL-Lite and Explanations for DL-Lite
• Explanations for traditional services
• Explanations for c...
Explanations
3 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Explanations
Why explanations?
3 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Explanations
Why explanations?
What are explanations?
3 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Explanations
Why explanations?
What are explanations?
• Explanations are formal proofs, constructed
from premises using ru...
Explanations
Why explanations?
What are explanations?
• Explanations are formal proofs, constructed
from premises using ru...
Explanations
Why explanations?
What are explanations?
• Explanations are formal proofs, constructed
from premises using ru...
Explanations (cont.)
4 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Explanations (cont.)
Audience: KB developer, End user
4 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Explanations (cont.)
Audience: KB developer, End user
4
1. Style. Understandable inference rules (NOT
refutation or resolu...
Explanations (cont.)
Audience: KB developer, End user
4
1. Style. Understandable inference rules (NOT
refutation or resolu...
Explanations (cont.)
Audience: KB developer, End user
4
1. Style. Understandable inference rules (NOT
refutation or resolu...
DL-Litef
Concept constructs
B ::= A | ƎP | ƎP-
C::= B | ¬B | C1 ⊓ C2
TBox Assertions
B ⊑ C
(funct P) (funt P-)
ABox Assert...
DL-Litef
Is-A Hierarchies
Class disjointness
Role-typing
Participation constraints
Non-participation constraints
Functiona...
DL-Litef
A1 ⊑ A2
A1 ⊑ ¬A2
ƎP ⊑ A1
ƎP- ⊑ A1
A1 ⊑ ƎP
A1 ⊑ ƎP-
A1 ⊑ ¬ƎP
A1 ⊑ ¬ƎP-
(funct P) (funct P-)
A1 ⊑ A2
disjoint(A1,A2...
Reasoning services
7 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Reasoning services
• Standard Inferences
• TBox reasoning (concept consistency, subsumption)
• ABox reasoning (KB satisfiab...
Reasoning services
• Standard Inferences
• TBox reasoning (concept consistency, subsumption)
• ABox reasoning (KB satisfiab...
Reasoning services
• Standard Inferences
• TBox reasoning (concept consistency, subsumption)
• ABox reasoning (KB satisfiab...
Reasoning services
• Standard Inferences
• TBox reasoning (concept consistency, subsumption)
• ABox reasoning (KB satisfiab...
B C
A
D
Concept Subsumption
8 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
B C
A
D
Concept Subsumption
• Hierarchy Traversing
8 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
B C
A
D
Concept Subsumption
• Hierarchy Traversing
A ⊑ D ⊓ C
8 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
B C
A
D
Concept Subsumption
• Hierarchy Traversing
A ⊑ D ⊓ C
A ⊑ C
A ⊑ B
B ⊑ D
8 ODBASE 08 - Monterrey, México
Thursday, A...
B C
A
D
Concept Subsumption
• Hierarchy Traversing
A ⊑ D ⊓ C
A ⊑ C
A ⊑ B
B ⊑ D
• Minimal size explanations
8 ODBASE 08 - M...
B1
C2
C1
A
C3
B2
B3
disjoint
n j
9
A is unsatisfiable
ODBASE 08 - Monterrey, México
Thursday, August 8, 13
B1
C2
C1
A
C3
B2
B3
disjoint
n j
9
Explanation
length
n + j = 6
A is unsatisfiable
ODBASE 08 - Monterrey, México
Thursday, ...
B1
C2
C1
A
E3
E2
E1D1
C3
E4
B2
B3
disjoint
disjoint
n j k l
10
A is unsatisfiable
ODBASE 08 - Monterrey, México
Thursday, A...
B1
C2
C1
A
E3
E2
E1D1
C3
E4
B2
B3
disjoint
disjoint
Explanation
length
k + l = 5
Explanation
length
n + j = 6
n j k l
10
A...
KB is inconsistent
11
1. PhD ⊑ Student
2. disjoint(Professor, Student)
3. range(supervisedBy) ⊑ Professor
4. PhD(al)
5. su...
KB is inconsistent
11
1. PhD ⊑ Student
2. disjoint(Professor, Student)
3. range(supervisedBy) ⊑ Professor
4. PhD(al)
5. su...
KB is inconsistent
11
1. PhD ⊑ Student
2. disjoint(Professor, Student)
3. range(supervisedBy) ⊑ Professor
4. PhD(al)
5. su...
KB is inconsistent
11
1. PhD ⊑ Student
2. disjoint(Professor, Student)
3. range(supervisedBy) ⊑ Professor
4. PhD(al)
5. su...
KB is inconsistent
11
1. PhD ⊑ Student
2. disjoint(Professor, Student)
3. range(supervisedBy) ⊑ Professor
4. PhD(al)
5. su...
Query Answering
• Successful queries
12 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
⋮
Student(bob)
Student(juan)
supervisedBy(tom, bob)
Student(al)
supervisedBy(tim, al)
teaches(al, ben)
teaches(sam, ben)
t...
⋮
Student(bob)
Student(juan)
supervisedBy(tom, bob)
Student(al)
supervisedBy(tim, al)
teaches(al, ben)
teaches(sam, ben)
t...
⋮
Student(bob)
Student(juan)
supervisedBy(tom, bob)
Student(al)
supervisedBy(tim, al)
teaches(al, ben)
teaches(sam, ben)
t...
1.PhD ⊑ Student
2.PhD ⊑ dom(supervisedBy)
3.range(supervisedBy) ⊑ Professor
4.Professor ⊑ domain(teaches)
5.PhD(al)
q(x) :...
1.PhD ⊑ Student
2.PhD ⊑ dom(supervisedBy)
3.range(supervisedBy) ⊑ Professor
4.Professor ⊑ domain(teaches)
5.PhD(al)
q(x) :...
al supervisedBy @1!!
1.PhD ⊑ Student
2.PhD ⊑ dom(supervisedBy)
3.range(supervisedBy) ⊑ Professor
4.Professor ⊑ domain(teac...
al supervisedBy @1!!
1.PhD ⊑ Student
2.PhD ⊑ dom(supervisedBy)
3.range(supervisedBy) ⊑ Professor
4.Professor ⊑ domain(teac...
al supervisedBy @1!!
al is in the domain of supervisedBy
1.PhD ⊑ Student
2.PhD ⊑ dom(supervisedBy)
3.range(supervisedBy) ⊑...
al supervisedBy @1!!
al is in the domain of supervisedBy
every PhD is also in the domain of supervisedBy ➔	 2
al is a PhD ...
al supervisedBy @1!!
al is in the domain of supervisedBy
every PhD is also in the domain of supervisedBy ➔	 2
al is a PhD ...
al supervisedBy @1!!
al is in the domain of supervisedBy
every PhD is also in the domain of supervisedBy ➔	 2
al is a PhD ...
al supervisedBy @1!!
al is in the domain of supervisedBy
every PhD is also in the domain of supervisedBy ➔	 2
al is a PhD ...
Query Answering
15 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Query Answering
• Successful queries
• Failed queries
15 ODBASE 08 - Monterrey, México
Thursday, August 8, 13
Query Answering
• Successful queries
• Failed queries
• Due to missing information
15 ODBASE 08 - Monterrey, México
Thursd...
Query Answering
• Successful queries
• Failed queries
• Due to missing information
• Due to unsatisfiability
15 ODBASE 08 -...
1.PhD ⊑ Student
2.range(supervisedBy) ⊑ Professor
3.disjoint(Professor,Student)
q(x):- PhD(x), supervisedBy(y, x)
q incons...
@1 is a Professor
@1 is a Student
1.PhD ⊑ Student
2.range(supervisedBy) ⊑ Professor
3.disjoint(Professor,Student)
q(x):- P...
@1 is a Professor
@1 is a Student
@1 is a PhD
every PhD is also a Student ➔	 1
1.PhD ⊑ Student
2.range(supervisedBy) ⊑ Pro...
@1 is a Professor
@1 is a Student
@1 is a PhD
every PhD is also a Student ➔	 1
1.PhD ⊑ Student
2.range(supervisedBy) ⊑ Pro...
@1 is a Professor
@2 supervisedBy @1
everything in the range of supervisedBy is a Professor ➔ 2
@1 is a Student
@1 is a Ph...
@1 is a Professor
@2 supervisedBy @1
everything in the range of supervisedBy is a Professor ➔ 2
@1 is a Student
@1 is a Ph...
Conclusions
• We addressed DL-Lite explanations can be given for
traditional reasoning services (shortness of proof).
• Fi...
Future Work
• Explanation of failed answers to CQs over
DL-Lite ontologies.
• Integration of prototype with the QuOnto
Rea...
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ODBASE'08 dl-lite explanations

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Explanations for DL-Lite, OWL 2 QL, reasoning in query rewriting

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ODBASE'08 dl-lite explanations

  1. 1. Explanations for DL-Lite Alexander Borgida 2 Diego Calvanese 1 Mariano Rodríguez-Muro 1 1 1 Free University of Bozen Bolzano 2 Rutgers University ODBASE 08 - Monterrey, México Thursday, August 8, 13
  2. 2. Outline • Explanations • DL-Lite and Explanations for DL-Lite • Explanations for traditional services • Explanations for conjunctive queries • Conclusions and future work 2 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  3. 3. Explanations 3 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  4. 4. Explanations Why explanations? 3 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  5. 5. Explanations Why explanations? What are explanations? 3 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  6. 6. Explanations Why explanations? What are explanations? • Explanations are formal proofs, constructed from premises using rules of inference. 3 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  7. 7. Explanations Why explanations? What are explanations? • Explanations are formal proofs, constructed from premises using rules of inference. 3 Features of an explanation: ODBASE 08 - Monterrey, México Thursday, August 8, 13
  8. 8. Explanations Why explanations? What are explanations? • Explanations are formal proofs, constructed from premises using rules of inference. 3 Features of an explanation: • Style • Length • Presentation ODBASE 08 - Monterrey, México Thursday, August 8, 13
  9. 9. Explanations (cont.) 4 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  10. 10. Explanations (cont.) Audience: KB developer, End user 4 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  11. 11. Explanations (cont.) Audience: KB developer, End user 4 1. Style. Understandable inference rules (NOT refutation or resolution) ODBASE 08 - Monterrey, México Thursday, August 8, 13
  12. 12. Explanations (cont.) Audience: KB developer, End user 4 1. Style. Understandable inference rules (NOT refutation or resolution) 2. Length: 'shorter' preferred ODBASE 08 - Monterrey, México Thursday, August 8, 13
  13. 13. Explanations (cont.) Audience: KB developer, End user 4 1. Style. Understandable inference rules (NOT refutation or resolution) 2. Length: 'shorter' preferred 3. Presentation: Complete proof vs Iterative process. as indicated by the user. Possibly eliminating 'obvious' parts (not addressed here) ODBASE 08 - Monterrey, México Thursday, August 8, 13
  14. 14. DL-Litef Concept constructs B ::= A | ƎP | ƎP- C::= B | ¬B | C1 ⊓ C2 TBox Assertions B ⊑ C (funct P) (funt P-) ABox Assertions A(a) R(a,b) 5 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  15. 15. DL-Litef Is-A Hierarchies Class disjointness Role-typing Participation constraints Non-participation constraints Functionality restrictions A1 ⊑ A2 A1 ⊑ ¬A2 ƎP ⊑ A1 ƎP- ⊑ A1 A1 ⊑ ƎP A1 ⊑ ƎP- A1 ⊑ ¬ƎP A1 ⊑ ¬ƎP- (funct P) (funct P-) 6 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  16. 16. DL-Litef A1 ⊑ A2 A1 ⊑ ¬A2 ƎP ⊑ A1 ƎP- ⊑ A1 A1 ⊑ ƎP A1 ⊑ ƎP- A1 ⊑ ¬ƎP A1 ⊑ ¬ƎP- (funct P) (funct P-) A1 ⊑ A2 disjoint(A1,A2) domain(P) ⊑ A1 range(P) ⊑ A1 A1 ⊑ domain(P) A1 ⊑ range(P) disjoint(A1, domain(P)) disjoint(A1, range(P)) (funct P) (funct P-) 6 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  17. 17. Reasoning services 7 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  18. 18. Reasoning services • Standard Inferences • TBox reasoning (concept consistency, subsumption) • ABox reasoning (KB satisfiability, Instance checking*) 7 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  19. 19. Reasoning services • Standard Inferences • TBox reasoning (concept consistency, subsumption) • ABox reasoning (KB satisfiability, Instance checking*) ✦ Finite model reasoning 7 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  20. 20. Reasoning services • Standard Inferences • TBox reasoning (concept consistency, subsumption) • ABox reasoning (KB satisfiability, Instance checking*) ✦ Finite model reasoning • Conjunctive Query Answering 7 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  21. 21. Reasoning services • Standard Inferences • TBox reasoning (concept consistency, subsumption) • ABox reasoning (KB satisfiability, Instance checking*) ✦ Finite model reasoning • Conjunctive Query Answering • Successful queries • Failed queries 7 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  22. 22. B C A D Concept Subsumption 8 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  23. 23. B C A D Concept Subsumption • Hierarchy Traversing 8 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  24. 24. B C A D Concept Subsumption • Hierarchy Traversing A ⊑ D ⊓ C 8 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  25. 25. B C A D Concept Subsumption • Hierarchy Traversing A ⊑ D ⊓ C A ⊑ C A ⊑ B B ⊑ D 8 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  26. 26. B C A D Concept Subsumption • Hierarchy Traversing A ⊑ D ⊓ C A ⊑ C A ⊑ B B ⊑ D • Minimal size explanations 8 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  27. 27. B1 C2 C1 A C3 B2 B3 disjoint n j 9 A is unsatisfiable ODBASE 08 - Monterrey, México Thursday, August 8, 13
  28. 28. B1 C2 C1 A C3 B2 B3 disjoint n j 9 Explanation length n + j = 6 A is unsatisfiable ODBASE 08 - Monterrey, México Thursday, August 8, 13
  29. 29. B1 C2 C1 A E3 E2 E1D1 C3 E4 B2 B3 disjoint disjoint n j k l 10 A is unsatisfiable ODBASE 08 - Monterrey, México Thursday, August 8, 13
  30. 30. B1 C2 C1 A E3 E2 E1D1 C3 E4 B2 B3 disjoint disjoint Explanation length k + l = 5 Explanation length n + j = 6 n j k l 10 A is unsatisfiable ODBASE 08 - Monterrey, México Thursday, August 8, 13
  31. 31. KB is inconsistent 11 1. PhD ⊑ Student 2. disjoint(Professor, Student) 3. range(supervisedBy) ⊑ Professor 4. PhD(al) 5. supevisedBy(tim, al) ODBASE 08 - Monterrey, México Thursday, August 8, 13
  32. 32. KB is inconsistent 11 1. PhD ⊑ Student 2. disjoint(Professor, Student) 3. range(supervisedBy) ⊑ Professor 4. PhD(al) 5. supevisedBy(tim, al) al is a Student al is a Professor no Student can be a Professor ➔ 2 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  33. 33. KB is inconsistent 11 1. PhD ⊑ Student 2. disjoint(Professor, Student) 3. range(supervisedBy) ⊑ Professor 4. PhD(al) 5. supevisedBy(tim, al) al is a Student !every PhD is also a Student ➔ 1 !al is a PhD ➔ 4 al is a Professor no Student can be a Professor ➔ 2 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  34. 34. KB is inconsistent 11 1. PhD ⊑ Student 2. disjoint(Professor, Student) 3. range(supervisedBy) ⊑ Professor 4. PhD(al) 5. supevisedBy(tim, al) al is a Student !every PhD is also a Student ➔ 1 !al is a PhD ➔ 4 al is a Professor everything in the range of supervisedBy is also a Professor ➔ 3 al is in range of supervisedBy no Student can be a Professor ➔ 2 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  35. 35. KB is inconsistent 11 1. PhD ⊑ Student 2. disjoint(Professor, Student) 3. range(supervisedBy) ⊑ Professor 4. PhD(al) 5. supevisedBy(tim, al) al is a Student !every PhD is also a Student ➔ 1 !al is a PhD ➔ 4 al is a Professor everything in the range of supervisedBy is also a Professor ➔ 3 al is in range of supervisedBy tim supervisedBy al ➔ 5 no Student can be a Professor ➔ 2 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  36. 36. Query Answering • Successful queries 12 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  37. 37. ⋮ Student(bob) Student(juan) supervisedBy(tom, bob) Student(al) supervisedBy(tim, al) teaches(al, ben) teaches(sam, ben) teaches(sam, john) teaches(sam, karl) ⋮ CQs in regular DBs q(x) :- Student(x), supervisedBy(y,x), teaches(x,z) 13 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  38. 38. ⋮ Student(bob) Student(juan) supervisedBy(tom, bob) Student(al) supervisedBy(tim, al) teaches(al, ben) teaches(sam, ben) teaches(sam, john) teaches(sam, karl) ⋮ CQs in regular DBs q(x) :- Student(x), supervisedBy(y,x), teaches(x,z) q(al) 13 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  39. 39. ⋮ Student(bob) Student(juan) supervisedBy(tom, bob) Student(al) supervisedBy(tim, al) teaches(al, ben) teaches(sam, ben) teaches(sam, john) teaches(sam, karl) ⋮ CQs in regular DBs q(x) :- Student(x), supervisedBy(y,x), teaches(x,z) q(al) Student(al), x=al supervisedBy(tim, al), y=tim teaches(al, ben), z = ben 13 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  40. 40. 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  41. 41. 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  42. 42. al supervisedBy @1!! 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 al is a Student q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  43. 43. al supervisedBy @1!! 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  44. 44. al supervisedBy @1!! al is in the domain of supervisedBy 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  45. 45. al supervisedBy @1!! al is in the domain of supervisedBy every PhD is also in the domain of supervisedBy ➔ 2 al is a PhD ➔ 5 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  46. 46. al supervisedBy @1!! al is in the domain of supervisedBy every PhD is also in the domain of supervisedBy ➔ 2 al is a PhD ➔ 5 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 every Professor is in the domain of teaches ➔ 4 @1 is a Professor al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  47. 47. al supervisedBy @1!! al is in the domain of supervisedBy every PhD is also in the domain of supervisedBy ➔ 2 al is a PhD ➔ 5 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 every Professor is in the domain of teaches ➔ 4 @1 is a Professor @1 is in the range of supervisedBy everything in the range of supervisedBy is a Professor ➔ 3 al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  48. 48. al supervisedBy @1!! al is in the domain of supervisedBy every PhD is also in the domain of supervisedBy ➔ 2 al is a PhD ➔ 5 1.PhD ⊑ Student 2.PhD ⊑ dom(supervisedBy) 3.range(supervisedBy) ⊑ Professor 4.Professor ⊑ domain(teaches) 5.PhD(al) @1 teaches @2 every Professor is in the domain of teaches ➔ 4 @1 is a Professor @1 is in the range of supervisedBy everything in the range of supervisedBy is a Professor ➔ 3 al is a Student every PhD is also a Student ➔ 1 al is a PhD ➔ 5 q(x) :- Student(x), supervisedBy(x,y), teaches(y,z) q(al) 14 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  49. 49. Query Answering 15 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  50. 50. Query Answering • Successful queries • Failed queries 15 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  51. 51. Query Answering • Successful queries • Failed queries • Due to missing information 15 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  52. 52. Query Answering • Successful queries • Failed queries • Due to missing information • Due to unsatisfiability 15 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  53. 53. 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  54. 54. @1 is a Professor @1 is a Student 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent q(@1) :- PhD(@1), supervisedBy(@2, @1) no Student can be a Professor ➔ 3 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  55. 55. @1 is a Professor @1 is a Student @1 is a PhD every PhD is also a Student ➔ 1 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent q(@1) :- PhD(@1), supervisedBy(@2, @1) no Student can be a Professor ➔ 3 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  56. 56. @1 is a Professor @1 is a Student @1 is a PhD every PhD is also a Student ➔ 1 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent q(@1) :- PhD(@1), supervisedBy(@2, @1) no Student can be a Professor ➔ 3 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  57. 57. @1 is a Professor @2 supervisedBy @1 everything in the range of supervisedBy is a Professor ➔ 2 @1 is a Student @1 is a PhD every PhD is also a Student ➔ 1 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent q(@1) :- PhD(@1), supervisedBy(@2, @1) no Student can be a Professor ➔ 3 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  58. 58. @1 is a Professor @2 supervisedBy @1 everything in the range of supervisedBy is a Professor ➔ 2 @1 is a Student @1 is a PhD every PhD is also a Student ➔ 1 1.PhD ⊑ Student 2.range(supervisedBy) ⊑ Professor 3.disjoint(Professor,Student) q(x):- PhD(x), supervisedBy(y, x) q inconsistent q(@1) :- PhD(@1), supervisedBy(@2, @1) no Student can be a Professor ➔ 3 16 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  59. 59. Conclusions • We addressed DL-Lite explanations can be given for traditional reasoning services (shortness of proof). • Finite model case. • Explaining conjunctive queries when reasoning is present by a) exploiting existing DL-Lite query rewriting algorithm and b) Prolog-based program. • We looked into the problem of explaining failed answers to queries. 17 ODBASE 08 - Monterrey, México Thursday, August 8, 13
  60. 60. Future Work • Explanation of failed answers to CQs over DL-Lite ontologies. • Integration of prototype with the QuOnto Reasoner. • Explanation in Ontology Based Data Access (presence of mappings). • Field testing of the algorithms. 18 ODBASE 08 - Monterrey, México Thursday, August 8, 13

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