1. Georg Gottlob
Computing Laboratory
Department of Computer Science
University of Oxford
Joint work with
G. Orsi and A. Pieris

5. 


8. D  reports(X,Y)  employee(X)
reports(john,ann) reports(X,Y)  employee(Y)
reports(ann,tom) reports(X,Y)  manager(Y,X)
manager(X,Y),manager(Y,Z)  manager(X,Z)
Intensional DB
reports(john,ann) reports(ann,tom)
employee(john) employee(ann)
employee(tom) manager(ann,john)
manager(tom,ann) manager(tom,john)
Q = XYZ employee(X),manager(X,Y),manager(Y,Z)

9. D  reports(X,Y)  employee(X)
reports(john,ann) reports(X,Y)  employee(Y)
reports(ann,tom) reports(X,Y)  manager(Y,X)
manager(X,Y),manager(Y,Z)  manager(X,Z)
Intensional DB
reports(john,ann) reports(ann,tom) Unique
employee(john) employee(ann) Least Herbrand Model
employee(tom) manager(ann,john) for
manager(tom,ann) manager(tom,john) Dυ
Q = XYZ employee(X),manager(X,Y),manager(Y,Z)

10. 

employee v supervisedBy
supervisedBy v employee
employee supervisedBy

12. employee v supervises-
supervises v employee

13. employee v supervises-
supervises v employee

14. employee v supervises-
supervises v employee
?:- supervises(X,John), employee(X)

15. employee v supervises-
supervises v employee
?:- supervises(X,John), employee(X)

16. employee v supervises-
supervises v employee
?:- supervises(John,X)

17. employee v supervises-
supervises v employee
?:- supervises(John,X)
Usually done with tableaux algorithms

18. 






19. 

22. DL axiom Datalog rule
Concept Inclusion
employee v person employee(X)  person(X)
(Inverse) Role Inclusion
reports¡ v manager reports(X,Y)  manager(Y,X)
Role Transitivity
trans(manager) manager(X,Y),manager(Y,Z)  manager(X,Z)

23. DL axiom Datalog(?) rule
Participation
employee v report employee(X)  Y report(X,Y)
Disjointness
employee v :customer employee(X),customer(X)  
Functionality
funct(reports) reports(X,Y),reports(X,Z)  Y = Z

28. 
D

29. Q = X (X)

D
D [  ² Q , B ( (B D [ )  B ² Q)
B¶DÆB²

30. Q = X (X)



D
D [  ² Q , B ( (B ² D[)  B ² Q)
B¶DÆB²

31. DB
technology
DLs
(DL-Lite, EL, Flogic Lite) +
constraints
Datalog

32.  



 

  

33.  
 υ

34.  
 υ


35. D
dom(D) = {a,b,c,d}
  
chase(D, ) = ?

36. D
dom(D) = {a,b,c,d}
  
chase(D, ) = D υ { r(b,z0)

37. D
dom(D) = {a,b,c,d}
  
chase(D, ) = D υ { r(b,z0), r(d,z1)

38. D
dom(D) = {a,b,c,d}
  
z0 = z1
chase(D, ) = D υ { r(b,z0), r(d,z1)

39. D
dom(D) = {a,b,c,d}
  
chase(D, ) = D υ { r(b,z1), r(d,z1) }

40. see, e.g.,
Deutsch, Nash & Remmel
chase(D,) PODS 08
D
h1 h2
. . .
M1
M2


41. Q h
chase(D,)
D
h1 h2
. . .
M1
M2
Dυ²Q , chase(D,) ² Q

42. Σ Σ Σ Σ Σ

43. 


44. 
Linear
DL-Lite
Sticky-join
Guarded
EL

46. 
Linear
DL-Lite
Sticky-join
FO-rewritable
Guarded
EL
PTIME

47. 
Linear
DL-Lite
Sticky-join
FO-rewritable
Guarded
EL
PTIME
We focus on the linear fragment:
• first-order rewriting
• semantic query optimizations

48. 


49. Q 
Q

50. Q 
Q* Q

51. Q 
Q* Q
D

52. DL-Lite: Popular family of DLs with highly tractable data complexity
DL-Lite TBox Datalog Representation
DL-Litecore
promoter v dealsWith professor(X)  Y teachesTo(X,Y)
promoter v customer professor(X),student(X)  
DL-LiteR
promotes¡ v isAdvertised promotes(X,Y)  isAdvertised(Y,X)
DL-LiteF
funct( supervises- ) supervises(Y,X),supervises Y,X  Y = Z

53.  

Q D


54.  

Q D


55.  


Q 


56.  
Q 
 
Q 

57.  

Q 
Q


58.  

Q 
Q



59.  

Q 
Q

 

60.  

Q 
Q

 


61.  

Q 
Q




62. Schema
SELECT promoter
FROM promotesTo PT, customer C
WHERE PT.promoted = C.name
UNION
SELECT promoter
FROM promotesTo PT1, promotesTo PT2
WHERE PT1.promoted = PT2.promoted
UNION
SELECT name
FROM promoter

63. Schema
Execute Q over D:
SELECT promoter
FROM promotesTo PT, customer C D
WHERE PT.promoted = C.name
UNION
SELECT promoter
FROM promotesTo PT1, promotesTo PT2
WHERE PT1.promoted = PT2.promoted
UNION
SELECT name
FROM promoter

64. : 






66. 


67. : 

 


68. : 

 



69. : 
 
 



70. : 
 
   
 


71. : 
 
   
 


72. 
: 

Q: 


74. : 






75. : 






77. 



78. 

79. 

82. 

83. 




84. 






85. 8-



86. EL: Popular DL for complex systems modelling (e.g., biology)
EL TBox Datalog Representation
 v 
u v 

87. 

88. 

89. 





92. 

94. 

9 

95. elephant(E),mouse(M)  biggerThan(E,M)

96. 



97. person v 9father¡
9father v person
?:- 9father.{John} u person

98. person v 9father¡
9father v person
?:- 9father.{John} u person
?:- 9father¡ u 9father.{John} u person

99. person v 9father¡
9father v person
?:- 9father.{John} u person
?:- 9father¡ u 9father.{John} u person
9father¡, 9father.{John}, person

100. person v 9father¡
9father v person
?:- 9father.{John} u person
?:- 9father¡ u 9father.{John} u person
9father¡, 9father.{John}, person
father

101. person v 9father¡
9father v person
?:- 9father.{John} u person
?:- 9father¡ u 9father.{John} u person
father
9father¡, 9father.{John}, person
father

102. person v 9father¡
9father v person
?:- 9father.{John} u person
Model true:- 9father¡ u 9father.{John} u person
father
9father¡, 9father.{John}, person
father

103. 


104. 


105. 


106. T 
E 
T , E

107. T 
E 
T , E

108. T 
E 
T , E