OWL 2 is widely used to describe complex objects such as chemical molecules; however, OWL 2 axioms cannot represent `structural' features of chemical entities such as having a ring. A combination of OWL 2, rules and \emph{description graphs} (DGs) has been suggested as a possible solution, but an attempt to apply this formalism in a chemical Semantic Web application has revealed several drawbacks. Based on this experience, we present a radically different approach to modelling complex objects via a novel formalism that we call Description Graph Logic Programs. At the syntactic level, our approach combines DGs, rules, and OWL 2 RL axioms, but we give semantics to our formalism via a translation into logic programs interpreted under stable model semantics. The result is an expressive formalism that is well suited for modelling objects with complex structure, that captures the OWL 2 RL profile, and that thus fits naturally into the Semantic Web landscape. Additionally, we test the practical feasibility of our approach by means of a prototypical implementation which provides encouraging results.

1. C LASSIFYING C HEMICALS U SING D ESCRIPTION
G RAPHS AND L OGIC P ROGRAMMING
Despoina Magka, Boris Motik and Ian Horrocks
Department of Computer Science, University of Oxford
May 28, 2012

2. O UTLINE
1 M OTIVATION
2 DGLP S , I MPLEMENTATION AND OVERVIEW
1

3. M ODELLING C HEMICALS WITH OWL
OWL used for the representation of molecular structures
2

4. M ODELLING C HEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds
[Villanueva-Rosales & Dumontier, OWLED 2007]
2

5. M ODELLING C HEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds
[Villanueva-Rosales & Dumontier, OWLED 2007]
Chemical information integration
[Konyk et al., DILS, 2008 ]
2

6. M ODELLING C HEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds
[Villanueva-Rosales & Dumontier, OWLED 2007]
Chemical information integration
[Konyk et al., DILS, 2008 ]
Subsumptions between molecules and chemical classes
[Hastings et al., OWLED, 2010]
2

7. T HE C H EBI O NTOLOGY
OWL ontology Chemical Entities of Biological Interest
3

8. T HE C H EBI O NTOLOGY
OWL ontology Chemical Entities of Biological Interest
Freely accessible dictionary of ‘small’ molecular entities
3

9. T HE C H EBI O NTOLOGY
OWL ontology Chemical Entities of Biological Interest
Freely accessible dictionary of ‘small’ molecular entities
High quality annotation and taxonomy of chemicals
3

10. T HE C H EBI O NTOLOGY
OWL ontology Chemical Entities of Biological Interest
Freely accessible dictionary of ‘small’ molecular entities
High quality annotation and taxonomy of chemicals
Interoperability between researchers
3

11. T HE C H EBI O NTOLOGY
OWL ontology Chemical Entities of Biological Interest
Freely accessible dictionary of ‘small’ molecular entities
High quality annotation and taxonomy of chemicals
Interoperability between researchers
Drug discovery and elucidation of metabolic pathways
3

12. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
4

13. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
4

14. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
4

15. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
4

16. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
4

17. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic?
4

18. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
4

19. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
4

20. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
4

21. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Speed up curating tasks with automated reasoning tools
4

22. AUTOMATE C HEMICAL C LASSIFICATION
ChEBI is manually incremented
Currently contains approx. 28,000 fully annotated entities
Grows at a rate of ~1,500 entities per curator per year
Biologically interesting entities possibly > 1,000,000
Each new molecule is subsumed by several chemical
classes
Is dinitrogen inorganic? Yes
Does cyclobutane contain a four-membered ring? Yes
Is acetylene a hydrocarbon? Yes
Does benzaldehyde contain a benzene ring? Yes
Speed up curating tasks with automated reasoning tools
4

23. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
5

24. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
5

25. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
5

26. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
E XAMPLE
Cyclobutane ∃(= 4)hasAtom.(Carbon ∃(= 2)hasBond.Carbon)
C C
C C
5

27. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
E XAMPLE
Cyclobutane ∃(= 4)hasAtom.(Carbon ∃(= 2)hasBond.Carbon)
C C
C C
5

28. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
E XAMPLE
Cyclobutane ∃(= 4)hasAtom.(Carbon ∃(= 2)hasBond.Carbon)
C C
C C
5

29. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
E XAMPLE
Cyclobutane ∃(= 4)hasAtom.(Carbon ∃(= 2)hasBond.Carbon)
C C
C C
OWL-based reasoning support
5

30. (M IS )R EPRESENTING R INGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWL
knowledge base
E XAMPLE
Cyclobutane ∃(= 4)hasAtom.(Carbon ∃(= 2)hasBond.Carbon)
C C
C C
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?
Does benzaldehyde contain a benzene ring?
5

31. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
6

32. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
6

33. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
6

34. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
6

35. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
Does cyclobutadiene have a conjugated four-membered
ring?
6

36. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
Does cyclobutadiene have a conjugated four-membered
ring?
6

37. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
Oxygen
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
6

38. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
Oxygen
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
∀hasAtom.(Carbon Hydrogen) Hydrocarbon
6

39. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
Oxygen
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
∀hasAtom.(Carbon Hydrogen) Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6

40. OWL E XTENSIONS
Limitation of OWL to represent cycles (partially) remedied
by extension of OWL with Description Graphs and rules
[Motik et al., 2009]
A Description Graph represents structures by means of a
directed labeled graph
E XAMPLE
Cyclobutadiene 1
Oxygen
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
∀hasAtom.(Carbon Hydrogen) Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6

41. R ESULTS OVERVIEW
Key idea:
7

42. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
7

43. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
7

44. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
7

45. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information
7

46. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information (e.g. hydrocarbons, inorganic molecules,
saturated compounds,. . . )
7

47. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information (e.g. hydrocarbons, inorganic molecules,
saturated compounds,. . . )
2 Represent rings with adequate precision
7

48. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information (e.g. hydrocarbons, inorganic molecules,
saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,
benzene rings,. . . )
7

49. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information (e.g. hydrocarbons, inorganic molecules,
saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,
benzene rings,. . . )
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
7

50. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence of
information (e.g. hydrocarbons, inorganic molecules,
saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,
benzene rings,. . . )
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
Prototypical implementation of a logic-based chemical
classification software
7

51. O UTLINE
1 M OTIVATION
2 DGLP S , I MPLEMENTATION AND OVERVIEW
8

52. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
9

53. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
9

54. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
E XAMPLE
Cyclobutane 1
O O
Dioxygen 1
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon Oxygen 2 3 Oxygen
9

55. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
9

56. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
E XAMPLE
Bond(x, y) → Bond(y, x)
SingleBond(x, y) → Bond(x, y)
9

57. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
E XAMPLE
Bond(x, y) → Bond(y, x)
SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
9

58. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
E XAMPLE
Bond(x, y) → Bond(y, x)
SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
E XAMPLE
HasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)
Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
9

59. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
E XAMPLE
Bond(x, y) → Bond(y, x)
SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
E XAMPLE
HasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)
Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
Facts
9

60. W HAT IS A DGLP O NTOLOGY ?
The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rules
E XAMPLE
Bond(x, y) → Bond(y, x)
SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
E XAMPLE
HasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)
Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
Facts
E XAMPLE
Cyclobutane(c1 ), Dinitrogen(c2 ), . . .
9

61. E NCODING D ESCRIPTION G RAPHS
Translate DGs into logic programs with function symbols
10

62. E NCODING D ESCRIPTION G RAPHS
Translate DGs into logic programs with function symbols
E XAMPLE
10

63. E NCODING D ESCRIPTION G RAPHS
Translate DGs into logic programs with function symbols
E XAMPLE
Cyclobutane(x) →Gcb (x, f1 (x), f2 (x), f3 (x), f4 (x))
Gcb (x, y1 , y2 , y3 , y4 ) →Cyclobutane(x) ∧
Carbon(y1 ) ∧ Carbon(y2 ) ∧
Carbon(y3 ) ∧ Carbon(y4 ) ∧
HasAtom(x, y1 ) ∧ Bond(y1 , y2 ) ∧
HasAtom(x, y2 ) ∧ Bond(y2 , y3 ) ∧
HasAtom(x, y3 ) ∧ Bond(y3 , y4 ) ∧
HasAtom(x, y4 ) ∧ Bond(y4 , y1 )
10

64. E NCODING D ESCRIPTION G RAPHS
Translate DGs into logic programs with function symbols
E XAMPLE
Cyclobutane(x) →Gcb (x, f1 (x), f2 (x), f3 (x), f4 (x))
Gcb (x, y1 , y2 , y3 , y4 ) →Cyclobutane(x) ∧
Carbon(y1 ) ∧ Carbon(y2 ) ∧
Carbon(y3 ) ∧ Carbon(y4 ) ∧
HasAtom(x, y1 ) ∧ Bond(y1 , y2 ) ∧
HasAtom(x, y2 ) ∧ Bond(y2 , y3 ) ∧
HasAtom(x, y3 ) ∧ Bond(y3 , y4 ) ∧
HasAtom(x, y4 ) ∧ Bond(y4 , y1 )
Function symbols allow for schema-level reasoning
10

65. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)
→ NotHydroCarbon(x)
Molecule(x) ∧ not NotHydroCarbon(x) → HydroCarbon(x)
11

66. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)
→ NotHydroCarbon(x)
Molecule(x) ∧ not NotHydroCarbon(x) → HydroCarbon(x)
C C
C C
11

67. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)
→ NotHydroCarbon(x)
Molecule(x) ∧ not NotHydroCarbon(x) → HydroCarbon(x)
Is cyclobutane a
C C hydrocarbon?
C C
11

68. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, yi ) ∧ Bond(yi , yi+1 ) ∧
1≤i≤4 1≤i≤3
Bond(y4 , y1 ) not yi = yj
1≤ij≤4
→ MoleculeWith4MemberedRing(x)
12

69. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, yi ) ∧ Bond(yi , yi+1 ) ∧
1≤i≤4 1≤i≤3
Bond(y4 , y1 ) not yi = yj
1≤ij≤4
→ MoleculeWith4MemberedRing(x)
C C
C C
12

70. C LASSIFYING C HEMICALS
E XAMPLE
Molecule(x) ∧ HasAtom(x, yi ) ∧ Bond(yi , yi+1 ) ∧
1≤i≤4 1≤i≤3
Bond(y4 , y1 ) not yi = yj
1≤ij≤4
→ MoleculeWith4MemberedRing(x)
Does cyclobutane contain a
C C four-membered ring?
C C
12

71. U NDECIDABILITY
Logic programs with function symbols can axiomatise
infinitely large structures
13

72. U NDECIDABILITY
Logic programs with function symbols can axiomatise
infinitely large structures
Reasoning with DGLP ontologies is trivially undecidable
13

73. U NDECIDABILITY
Logic programs with function symbols can axiomatise
infinitely large structures
Reasoning with DGLP ontologies is trivially undecidable
We are only interested in finite structures
13

74. U NDECIDABILITY
Logic programs with function symbols can axiomatise
infinitely large structures
Reasoning with DGLP ontologies is trivially undecidable
We are only interested in finite structures
E XAMPLE
Carboxyl
O AceticAcid Carboxyl
Carbonyl 1 1
C
Methyl Hydroxyl
2 3 2 3
CH3 OH Methyl Carboxyl Carbonyl Hydroxyl
13

75. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
14

76. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
14

77. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
14

78. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
14

79. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
E XAMPLE
Carboxyl
O AceticAcid Carboxyl
Carbonyl 1 1
C
Methyl Hydroxyl
2 3 2 3
CH3 OH Methyl Carboxyl Carbonyl Hydroxyl
14

80. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
Novel semantic acyclicity condition
14

81. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
Novel semantic acyclicity condition
checks for generation of unbounded structures on the fly
14

82. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
Novel semantic acyclicity condition
checks for generation of unbounded structures on the fly
modelling of molecules that contain functional groups
14

83. ACYCLICITY C ONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]
super-weak acyclicity [Marnette, PODS, 2009]
joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]
rule out naturally-arising nested structures
Novel semantic acyclicity condition
checks for generation of unbounded structures on the fly
modelling of molecules that contain functional groups
O
Carbonyl
C
Methyl Hydroxyl
CH3 OH
Carboxyl
14

84. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
15

85. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
15

86. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
15

87. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
15

88. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
15

89. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
Results:
15

90. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
Results:
All DGLP ontologies were found acyclic
15

91. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
Results:
All DGLP ontologies were found acyclic
Molecules classified as expected
15

92. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
Hydrocarbons
Inorganic molecules
Molecules with exactly two carbons
Molecules with a four-membered ring
Molecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
Results:
All DGLP ontologies were found acyclic
Molecules classified as expected
Suite of subsumption tests for largest ontology performed in
few minutes
15

93. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
16

94. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
16

95. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
16

96. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
16

97. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
16

98. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Future directions:
16

99. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the head
16

100. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the head
User-friendly surface syntax
16

101. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the head
User-friendly surface syntax
Fully-fledged chemical classification system
16

102. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
2 Novel acyclicity condition for logic programs with restricted
use of function symbols
3 Prototype for the automated classification of chemicals
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the head
User-friendly surface syntax
Fully-fledged chemical classification system
Thank you for listening. Questions?
16