This document outlines a method for modeling structured domains like molecules and chemical entities using description graphs and logic programming. It discusses limitations of representing cyclic structures like chemical rings in OWL and proposes an extension called Description Graph Logic Programs (DGLPs) that uses description graphs and logic programming semantics. DGLPs provide an expressive yet decidable logic-based formalism that can represent all cycles using a closed-world assumption, addressing issues in modeling domains with complex interconnected structures in OWL.

1. M ODELLING S TRUCTURED D OMAINS 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 29, 2012

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

3. M ODELLING S TRUCTURED D OMAINS WITH OWL
OWL used for the representation of complex structures:
2

4. M ODELLING S TRUCTURED D OMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
2

5. M ODELLING S TRUCTURED D OMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
2

6. M ODELLING S TRUCTURED D OMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
2

7. M ODELLING S TRUCTURED D OMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2

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

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

12. 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

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

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

23. 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

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

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

31. (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

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]
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
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
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
C C Carbon 2 3 Carbon
C C Carbon 5 4 Carbon
Does cyclobutadiene have a conjugated four-membered
ring?
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
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
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. 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

42. R ESULTS OVERVIEW
Key idea:
7

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

44. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
7

45. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
7

46. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
DGLP S all cycles CWA
OWL+DG S + RULES some cycles OWA
OWL no cycles OWA
7

47. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
DGLP S all cycles CWA
OWL+DG S + RULES some cycles OWA
OWL no cycles OWA
Negation-as-failure ↔ Closed-world assumption ↔ Missing
information treated as false
7

48. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
DGLP S all cycles CWA
OWL+DG S + RULES some cycles OWA
OWL no cycles OWA
Negation-as-failure ↔ Closed-world assumption ↔ Missing
information treated as false
Classical negation ↔ Open-world assumption ↔ Missing
information treated as not known
7

49. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
DGLP S all cycles CWA
OWL+DG S + RULES some cycles OWA
OWL no cycles OWA
Prototypical implementation of DGLPs with application in
structure-based chemical classification
7

50. R ESULTS OVERVIEW
Key idea:
Switch from first-order logic to logic programming semantics
Use negation-as-failure to derive non-monotonic inferences
Expressive decidable logic-based formalism for modelling
structured entities: Description Graph Logic Programs
(DGLPs)
DGLP S all cycles CWA
OWL+DG S + RULES some cycles OWA
OWL no cycles OWA
Prototypical implementation of DGLPs with application in
structure-based chemical classification
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. C LASSIFYING O BJECTS
E XAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)
→ NotHydroCarbon(x)
Molecule(x) ∧ not NotHydroCarbon(x) → HydroCarbon(x)
11

65. C LASSIFYING O BJECTS
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

66. C LASSIFYING O BJECTS
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

67. C LASSIFYING O BJECTS
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

68. C LASSIFYING O BJECTS
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

69. C LASSIFYING O BJECTS
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

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

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

72. 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

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
E XAMPLE
Carboxyl
O AceticAcid Carboxyl
Carbonyl 1 1
C
Methyl Hydroxyl
2 3 2 3
CH3 OH Methyl Carboxyl Carbonyl Hydroxyl
13

74. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
14

75. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databases
14

76. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databases
Various syntax-based acyclicity conditions
14

77. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databases
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. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databases
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. S YNTACTIC ACYCLICITY C ONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databases
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. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
15

81. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
E XAMPLE
AceticAcid Carboxyl
1 1
AceticAcid Carboxyl
2 3 2 3
Methyl Carboxyl Carbonyl Hydroxyl
15

82. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
2 Extend the logic program with rules that detect violation of
the graph ordering
15

83. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
2 Extend the logic program with rules that detect violation of
the graph ordering
3 Repetitive construction of graph instances during reasoning
triggers derivation of Cycle
15

84. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
2 Extend the logic program with rules that detect violation of
the graph ordering
3 Repetitive construction of graph instances during reasoning
triggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O |= Cycle
15

85. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
2 Extend the logic program with rules that detect violation of
the graph ordering
3 Repetitive construction of graph instances during reasoning
triggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O |= Cycle
DGLP ontology with acetic acid is semantically acyclic
15

86. S EMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifies
which graph instances may imply the existence of other
graph instances
2 Extend the logic program with rules that detect violation of
the graph ordering
3 Repetitive construction of graph instances during reasoning
triggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O |= Cycle
DGLP ontology with acetic acid is semantically acyclic
O
Carbonyl
C
Methyl Hydroxyl
CH3 OH
Carboxyl
15

87. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
16

88. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
16

89. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
16

90. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratified
negation capture a wide range of chemical classes:
16

91. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratified
negation capture a wide range of chemical classes:
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
16

92. T ECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratified
negation capture a wide range of chemical classes:
Is dinitrogen inorganic?
Does cyclobutane contain a four-membered ring?
Is acetylene a hydrocarbon?
Does benzaldehyde contain a benzene ring?
16

93. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
17

94. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
17

95. E MPIRICAL E VALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engine
Chemical classes:
17

96. 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
17

97. 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
17

98. 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:
17

99. 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
17

100. 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
17

101. 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
17

102. OVERVIEW AND F UTURE D IRECTIONS
1 Expressive and decidable formalism for representation of
structured objects
18

103. 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
18

104. 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 structure-based classification of complex
objects
18

105. 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 structure-based classification of complex
objects
Future directions:
Generalise acyclicity condition for datalog rules with
existentials in the head
18

106. 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 structure-based classification of complex
objects
Future directions:
Generalise acyclicity condition for datalog rules with
existentials in the head
Relax stratifiability criteria for negation
18

107. 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 structure-based classification of complex
objects
Future directions:
Generalise acyclicity condition for datalog rules with
existentials in the head
Relax stratifiability criteria for negation
User-friendly surface syntax
18

108. 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 structure-based classification of complex
objects
Future directions:
Generalise acyclicity condition for datalog rules with
existentials in the head
Relax stratifiability criteria for negation
User-friendly surface syntax
Fully-fledged classification system for graph-shaped objects
18

109. 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 structure-based classification of complex
objects
Future directions:
Generalise acyclicity condition for datalog rules with
existentials in the head
Relax stratifiability criteria for negation
User-friendly surface syntax
Fully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18