M ODELLING S TRUCTURED D OMAINS U SING    D ESCRIPTION G RAPHS AND L OGIC             P ROGRAMMING   Despoina Magka, Boris...
O UTLINE    1   M OTIVATION    2   DGLP S , I MPLEMENTATION AND OVERVIEW1
M ODELLING S TRUCTURED D OMAINS WITH OWL      OWL used for the representation of complex structures:2
M ODELLING S TRUCTURED D OMAINS WITH OWL      OWL used for the representation of complex structures:        Aerospace2
M ODELLING S TRUCTURED D OMAINS WITH OWL      OWL used for the representation of complex structures:        Aerospace     ...
M ODELLING S TRUCTURED D OMAINS WITH OWL      OWL used for the representation of complex structures:        Aerospace     ...
M ODELLING S TRUCTURED D OMAINS WITH OWL      OWL used for the representation of complex structures:        Aerospace     ...
T HE C H EBI O NTOLOGY    OWL ontology Chemical Entities of Biological Interest3
T HE C H EBI O NTOLOGY    OWL ontology Chemical Entities of Biological Interest        Freely accessible dictionary of ‘sm...
T HE C H EBI O NTOLOGY    OWL ontology Chemical Entities of Biological Interest        Freely accessible dictionary of ‘sm...
T HE C H EBI O NTOLOGY    OWL ontology Chemical Entities of Biological Interest        Freely accessible dictionary of ‘sm...
T HE C H EBI O NTOLOGY    OWL ontology Chemical Entities of Biological Interest        Freely accessible dictionary of ‘sm...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented4
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
AUTOMATE C HEMICAL C LASSIFICATION    ChEBI is manually incremented    Currently contains approx. 28,000 fully annotated e...
(M IS )R EPRESENTING R INGS WITH OWL    Chemical compounds with rings are highly frequent5
(M IS )R EPRESENTING R INGS WITH OWL    Chemical compounds with rings are highly frequent    Fundamental inability of OWL ...
(M IS )R EPRESENTING R INGS WITH OWL    Chemical compounds with rings are highly frequent    Fundamental inability of OWL ...
(M IS )R EPRESENTING R INGS WITH OWL          Chemical compounds with rings are highly frequent          Fundamental inabi...
(M IS )R EPRESENTING R INGS WITH OWL          Chemical compounds with rings are highly frequent          Fundamental inabi...
(M IS )R EPRESENTING R INGS WITH OWL          Chemical compounds with rings are highly frequent          Fundamental inabi...
(M IS )R EPRESENTING R INGS WITH OWL          Chemical compounds with rings are highly frequent          Fundamental inabi...
(M IS )R EPRESENTING R INGS WITH OWL          Chemical compounds with rings are highly frequent          Fundamental inabi...
OWL E XTENSIONS    Limitation of OWL to represent cycles (partially) remedied    by extension of OWL with Description Grap...
OWL E XTENSIONS    Limitation of OWL to represent cycles (partially) remedied    by extension of OWL with Description Grap...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
OWL E XTENSIONS         Limitation of OWL to represent cycles (partially) remedied         by extension of OWL with Descri...
R ESULTS OVERVIEW    Key idea:7
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics7
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
R ESULTS OVERVIEW    Key idea:        Switch from first-order logic to logic programming semantics        Use negation-as-f...
O UTLINE    1   M OTIVATION    2   DGLP S , I MPLEMENTATION AND OVERVIEW8
W HAT IS A DGLP O NTOLOGY ?    The syntactic objects of a DGLP ontology:9
W HAT IS A DGLP O NTOLOGY ?    The syntactic objects of a DGLP ontology:        Description graphs9
W HAT IS A DGLP O NTOLOGY ?         The syntactic objects of a DGLP ontology:             Description graphs    E XAMPLE  ...
W HAT IS A DGLP O NTOLOGY ?    The syntactic objects of a DGLP ontology:        Description graphs        Function-free FO...
W HAT IS A DGLP O NTOLOGY ?       The syntactic objects of a DGLP ontology:            Description graphs            Funct...
W HAT IS A DGLP O NTOLOGY ?       The syntactic objects of a DGLP ontology:            Description graphs            Funct...
W HAT IS A DGLP O NTOLOGY ?       The syntactic objects of a DGLP ontology:            Description graphs            Funct...
W HAT IS A DGLP O NTOLOGY ?       The syntactic objects of a DGLP ontology:            Description graphs            Funct...
W HAT IS A DGLP O NTOLOGY ?       The syntactic objects of a DGLP ontology:            Description graphs            Funct...
E NCODING D ESCRIPTION G RAPHS     Translate DGs into logic programs with function symbols10
E NCODING D ESCRIPTION G RAPHS        Translate DGs into logic programs with function symbols     E XAMPLE10
E NCODING D ESCRIPTION G RAPHS        Translate DGs into logic programs with function symbols     E XAMPLE             Cyc...
C LASSIFYING O BJECTS     E XAMPLE     Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)     → NotHydroCarbon(...
C LASSIFYING O BJECTS     E XAMPLE     Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)     → NotHydroCarbon(...
C LASSIFYING O BJECTS     E XAMPLE     Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)     → NotHydroCarbon(...
C LASSIFYING O BJECTS     E XAMPLE       Molecule(x) ∧              HasAtom(x, yi ) ∧           Bond(yi , yi+1 ) ∧        ...
C LASSIFYING O BJECTS     E XAMPLE       Molecule(x) ∧              HasAtom(x, yi ) ∧           Bond(yi , yi+1 ) ∧        ...
C LASSIFYING O BJECTS     E XAMPLE       Molecule(x) ∧              HasAtom(x, yi ) ∧           Bond(yi , yi+1 ) ∧        ...
U NDECIDABILITY     Logic programs with function symbols can axiomatise     infinitely large structures13
U NDECIDABILITY     Logic programs with function symbols can axiomatise     infinitely large structures     Reasoning with ...
U NDECIDABILITY     Logic programs with function symbols can axiomatise     infinitely large structures     Reasoning with ...
U NDECIDABILITY        Logic programs with function symbols can axiomatise        infinitely large structures        Reason...
S YNTACTIC ACYCLICITY C ONDITIONS     Chase [Maier et al., 1979] termination is undecidable14
S YNTACTIC ACYCLICITY C ONDITIONS     Chase [Maier et al., 1979] termination is undecidable     Problem extensively studie...
S YNTACTIC ACYCLICITY C ONDITIONS     Chase [Maier et al., 1979] termination is undecidable     Problem extensively studie...
S YNTACTIC ACYCLICITY C ONDITIONS     Chase [Maier et al., 1979] termination is undecidable     Problem extensively studie...
S YNTACTIC ACYCLICITY C ONDITIONS     Chase [Maier et al., 1979] termination is undecidable     Problem extensively studie...
S YNTACTIC ACYCLICITY C ONDITIONS        Chase [Maier et al., 1979] termination is undecidable        Problem extensively ...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
S EMANTIC ACYCLICITY      1   Transitive and irreflexive graph ordering which specifies          which graph instances may i...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
S EMANTIC ACYCLICITY     1   Transitive and irreflexive graph ordering which specifies         which graph instances may imp...
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies16
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies     2   Decidability of semantic acyc...
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies     2   Decidability of semantic acyc...
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies     2   Decidability of semantic acyc...
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies     2   Decidability of semantic acyc...
T ECHNICAL RESULTS     1   Termination guarantee for semantically acyclic ontologies     2   Decidability of semantic acyc...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format17
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine17
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
E MPIRICAL E VALUATION     Data extracted from ChEBI in Molfile format     XSB logic programming engine     Chemical classe...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
OVERVIEW AND F UTURE D IRECTIONS     1   Expressive and decidable formalism for representation of         structured objec...
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Modelling Structured Domains with Description Graphs and Logic Programming

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Modelling Structured Domains with Description Graphs and Logic Programming

  1. 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. 2. O UTLINE 1 M OTIVATION 2 DGLP S , I MPLEMENTATION AND OVERVIEW1
  3. 3. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures:2
  4. 4. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace2
  5. 5. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology2
  6. 6. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology Human anatomy2
  7. 7. M ODELLING S TRUCTURED D OMAINS WITH OWL OWL used for the representation of complex structures: Aerospace Cellular biology Human anatomy Molecules2
  8. 8. T HE C H EBI O NTOLOGY OWL ontology Chemical Entities of Biological Interest3
  9. 9. T HE C H EBI O NTOLOGY OWL ontology Chemical Entities of Biological Interest Freely accessible dictionary of ‘small’ molecular entities3
  10. 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. 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. 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. 13. AUTOMATE C HEMICAL C LASSIFICATION ChEBI is manually incremented4
  14. 14. AUTOMATE C HEMICAL C LASSIFICATION ChEBI is manually incremented Currently contains approx. 28,000 fully annotated entities4
  15. 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. 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. 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. 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. 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. 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. 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. 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. 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. 24. (M IS )R EPRESENTING R INGS WITH OWL Chemical compounds with rings are highly frequent5
  25. 25. (M IS )R EPRESENTING R INGS WITH OWL Chemical compounds with rings are highly frequent Fundamental inability of OWL to represent cycles5
  26. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 42. R ESULTS OVERVIEW Key idea:7
  43. 43. R ESULTS OVERVIEW Key idea: Switch from first-order logic to logic programming semantics7
  44. 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. 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. 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. 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. 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. 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. 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. 51. O UTLINE 1 M OTIVATION 2 DGLP S , I MPLEMENTATION AND OVERVIEW8
  52. 52. W HAT IS A DGLP O NTOLOGY ? The syntactic objects of a DGLP ontology:9
  53. 53. W HAT IS A DGLP O NTOLOGY ? The syntactic objects of a DGLP ontology: Description graphs9
  54. 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. 55. W HAT IS A DGLP O NTOLOGY ? The syntactic objects of a DGLP ontology: Description graphs Function-free FOL Horn rules9
  56. 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. 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. 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. 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. 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. 61. E NCODING D ESCRIPTION G RAPHS Translate DGs into logic programs with function symbols10
  62. 62. E NCODING D ESCRIPTION G RAPHS Translate DGs into logic programs with function symbols E XAMPLE10
  63. 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. 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. 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. 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. 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. 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 C12
  69. 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 C12
  70. 70. U NDECIDABILITY Logic programs with function symbols can axiomatise infinitely large structures13
  71. 71. U NDECIDABILITY Logic programs with function symbols can axiomatise infinitely large structures Reasoning with DGLP ontologies is trivially undecidable13
  72. 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. 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. 74. S YNTACTIC ACYCLICITY C ONDITIONS Chase [Maier et al., 1979] termination is undecidable14
  75. 75. S YNTACTIC ACYCLICITY C ONDITIONS Chase [Maier et al., 1979] termination is undecidable Problem extensively studied in theory of databases14
  76. 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. 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. 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. 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. 80. S EMANTIC ACYCLICITY 1 Transitive and irreflexive graph ordering which specifies which graph instances may imply the existence of other graph instances15
  81. 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. 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. 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. 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. 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. 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. 87. T ECHNICAL RESULTS 1 Termination guarantee for semantically acyclic ontologies16
  88. 88. T ECHNICAL RESULTS 1 Termination guarantee for semantically acyclic ontologies 2 Decidability of semantic acyclicity for negation-free DGLP ontologies16
  89. 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. 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. 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. 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. 93. E MPIRICAL E VALUATION Data extracted from ChEBI in Molfile format17
  94. 94. E MPIRICAL E VALUATION Data extracted from ChEBI in Molfile format XSB logic programming engine17
  95. 95. E MPIRICAL E VALUATION Data extracted from ChEBI in Molfile format XSB logic programming engine Chemical classes:17
  96. 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. 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. 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. 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. 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. 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. 102. OVERVIEW AND F UTURE D IRECTIONS 1 Expressive and decidable formalism for representation of structured objects18
  103. 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. 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. 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. 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. 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. 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. 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

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