Modelling Structured Domains with Description Graphs and Logic Programming

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  • 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 OVERVIEW1
  • 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: Aerospace2
  • 5. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology2
  • 6. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology Human anatomy2
  • 7. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology Human anatomy Molecules2
  • 8. T HE C H EBI O NTOLOGY OWL ontology Chemical Entities of Biological Interest3
  • 9. T HE C H EBI O NTOLOGY OWL ontology Chemical Entities of Biological Interest Freely accessible dictionary of ‘small’ molecular entities3
  • 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 chemicals3
  • 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 researchers3
  • 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 pathways3
  • 13. AUTOMATE C HEMICAL C LASSIFICATION ChEBI is manually incremented4
  • 14. AUTOMATE C HEMICAL C LASSIFICATION ChEBI is manually incremented Currently contains approx. 28,000 fully annotated entities4
  • 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 year4
  • 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 > 1,000,0004
  • 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 classes4
  • 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 tools4
  • 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 tools4
  • 24. (M IS )R EPRESENTING R INGS WITH OWL Chemical compounds with rings are highly frequent5
  • 25. (M IS )R EPRESENTING R INGS WITH OWL Chemical compounds with rings are highly frequent Fundamental inability of OWL to represent cycles5
  • 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 base5
  • 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 C5
  • 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 C5
  • 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 C5
  • 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 support5
  • 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 graph6
  • 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 Carbon6
  • 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 Carbon6
  • 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 Carbon6
  • 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) Hydrocarbon6
  • 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 semantics7
  • 44. R ESULTS OVERVIEW Key idea: Switch from first-order logic to logic programming semantics Use negation-as-failure to derive non-monotonic inferences7
  • 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 OWA7
  • 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 false7
  • 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 known7
  • 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 classification7
  • 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 classification7
  • 51. O UTLINE 1 M OTIVATION 2 DGLP S , I MPLEMENTATION AND OVERVIEW8
  • 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 graphs9
  • 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 Oxygen9
  • 55. W HAT IS A DGLP O NTOLOGY ? The syntactic objects of a DGLP ontology: Description graphs Function-free FOL Horn rules9
  • 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-failure9
  • 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) Facts9
  • 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 symbols10
  • 62. E NCODING D ESCRIPTION G RAPHS Translate DGs into logic programs with function symbols E XAMPLE10
  • 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 C11
  • 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 C11
  • 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≤i<j≤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≤i<j≤4 → MoleculeWith4MemberedRing(x) C C C C12
  • 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≤i<j≤4 → MoleculeWith4MemberedRing(x) Does cyclobutane contain a C C four-membered ring?  C C12
  • 70. U NDECIDABILITY Logic programs with function symbols can axiomatise infinitely large structures13
  • 71. U NDECIDABILITY Logic programs with function symbols can axiomatise infinitely large structures Reasoning with DGLP ontologies is trivially undecidable13
  • 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 structures13
  • 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 Hydroxyl13
  • 74. S YNTACTIC ACYCLICITY C ONDITIONS Chase [Maier et al., 1979] termination is undecidable14
  • 75. S YNTACTIC ACYCLICITY C ONDITIONS Chase [Maier et al., 1979] termination is undecidable Problem extensively studied in theory of databases14
  • 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 conditions14
  • 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 structures14
  • 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 Hydroxyl14
  • 80. S EMANTIC ACYCLICITY 1 Transitive and irreflexive graph ordering which specifies which graph instances may imply the existence of other graph instances15
  • 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 Hydroxyl15
  • 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 ordering15
  • 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 Cycle15
  • 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 |= Cycle15
  • 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 Carboxyl15
  • 87. T ECHNICAL RESULTS 1 Termination guarantee for semantically acyclic ontologies16
  • 88. T ECHNICAL RESULTS 1 Termination guarantee for semantically acyclic ontologies 2 Decidability of semantic acyclicity for negation-free DGLP ontologies16
  • 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 negation16
  • 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 format17
  • 94. E MPIRICAL E VALUATION Data extracted from ChEBI in Molfile format XSB logic programming engine17
  • 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 benzene17
  • 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 molecules17
  • 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 acyclic17
  • 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 expected17
  • 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 minutes17
  • 102. OVERVIEW AND F UTURE D IRECTIONS 1 Expressive and decidable formalism for representation of structured objects18
  • 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 symbols18
  • 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 objects18
  • 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 head18
  • 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 negation18
  • 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 syntax18
  • 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 objects18
  • 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