modelling structured domains with description graphs and logic programming
TRANSCRIPT
MODELLING STRUCTURED DOMAINS USING
DESCRIPTION GRAPHS AND LOGIC
PROGRAMMING
Despoina Magka, Boris Motik and Ian Horrocks
Department of Computer Science, University of Oxford
May 29, 2012
OUTLINE
1 MOTIVATION
2 DGLPS, IMPLEMENTATION AND OVERVIEW
1
MODELLING STRUCTURED DOMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2
MODELLING STRUCTURED DOMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2
MODELLING STRUCTURED DOMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2
MODELLING STRUCTURED DOMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2
MODELLING STRUCTURED DOMAINS WITH OWL
OWL used for the representation of complex structures:
Aerospace
Cellular biology
Human anatomy
Molecules
2
THE CHEBI ONTOLOGY
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
THE CHEBI ONTOLOGY
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
THE CHEBI ONTOLOGY
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
THE CHEBI ONTOLOGY
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
THE CHEBI ONTOLOGY
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
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
AUTOMATE CHEMICAL CLASSIFICATION
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 chemicalclasses
Is dinitrogen inorganic? YesDoes cyclobutane contain a four-membered ring? YesIs acetylene a hydrocarbon? YesDoes benzaldehyde contain a benzene ring? Yes
Speed up curating tasks with automated reasoning tools
4
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequent
Fundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge baseOWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cycles
At least one tree-shaped model for each consistent OWLknowledge baseOWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
EXAMPLE
Cyclobutane v ∃(= 4)hasAtom.(Carbon u ∃(= 2)hasBond.Carbon)
C C
CC
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
EXAMPLE
Cyclobutane v ∃(= 4)hasAtom.(Carbon u ∃(= 2)hasBond.Carbon)
C C
CC
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
EXAMPLE
Cyclobutane v ∃(= 4)hasAtom.(Carbon u ∃(= 2)hasBond.Carbon)
C C
CC
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
EXAMPLE
Cyclobutane v ∃(= 4)hasAtom.(Carbon u ∃(= 2)hasBond.Carbon)
C C
CC
OWL-based reasoning support
Does cyclobutane contain a four-membered ring?Does benzaldehyde contain a benzene ring?
5
(MIS)REPRESENTING RINGS WITH OWL
Chemical compounds with rings are highly frequentFundamental inability of OWL to represent cyclesAt least one tree-shaped model for each consistent OWLknowledge base
EXAMPLE
Cyclobutane v ∃(= 4)hasAtom.(Carbon u ∃(= 2)hasBond.Carbon)
C C
CC
OWL-based reasoning support
Does cyclobutane contain a four-membered ring? 8
Does benzaldehyde contain a benzene ring? 8
5
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]
A Description Graph represents structures by means of adirected labeled graphIs cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Does cyclobutadiene have a conjugated four-memberedring?
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Does cyclobutadiene have a conjugated four-memberedring? 3
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
Oxygen
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
Oxygen
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
Oxygen
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon?
6
OWL EXTENSIONS
Limitation of OWL to represent cycles (partially) remediedby extension of OWL with Description Graphs and rules[Motik et al., 2009]A Description Graph represents structures by means of adirected labeled graph
EXAMPLE
C C
CC
1Cyclobutadiene
2Carbon 3 Carbon
4 Carbon5Carbon
Oxygen
∀hasAtom.(Carbon t Hydrogen) v Hydrocarbon
Is cyclobutadiene a hydrocarbon? 8
6
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as false
Classical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
RESULTS 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 modellingstructured entities: Description Graph Logic Programs(DGLPs)
DGLPS all cycles CWAOWL+DGS+RULES some cycles OWAOWL no cycles OWA
Negation-as-failure↔ Closed-world assumption↔ Missinginformation treated as falseClassical negation ↔ Open-world assumption↔ Missinginformation treated as not known
Prototypical implementation of DGLPs with application instructure-based chemical classification
7
OUTLINE
1 MOTIVATION
2 DGLPS, IMPLEMENTATION AND OVERVIEW
8
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rulesRules with negation-as-failureFacts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphs
Function-free FOL Horn rulesRules with negation-as-failureFacts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphs
EXAMPLE
C C
CC
1Cyclobutane
2Carbon 3 Carbon
4 Carbon5Carbon
O O
1Dioxygen
2Oxygen 3 Oxygen
Function-free FOL Horn rulesRules with negation-as-failureFacts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
Rules with negation-as-failureFacts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
EXAMPLEBond(x, y) → Bond(y, x)SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failureFacts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
EXAMPLEBond(x, y) → Bond(y, x)SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
Facts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
EXAMPLEBond(x, y) → Bond(y, x)SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
EXAMPLEHasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
Facts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
EXAMPLEBond(x, y) → Bond(y, x)SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
EXAMPLEHasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
Facts
9
WHAT IS A DGLP ONTOLOGY?The syntactic objects of a DGLP ontology:
Description graphsFunction-free FOL Horn rules
EXAMPLEBond(x, y) → Bond(y, x)SingleBond(x, y) → Bond(x, y)
Rules with negation-as-failure
EXAMPLEHasAtom(x, y) ∧ Carbon(y) → HasCarbon(x)Molecule(x)∧ not HasCarbon(x) → Inorganic(x)
Facts
EXAMPLE
Cyclobutane(c1), Dinitrogen(c2), . . .
9
ENCODING DESCRIPTION GRAPHS
Translate DGs into logic programs with function symbols
10
ENCODING DESCRIPTION GRAPHS
Translate DGs into logic programs with function symbols
EXAMPLE
10
ENCODING DESCRIPTION GRAPHS
Translate DGs into logic programs with function symbols
EXAMPLE
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
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)→ NotHydroCarbon(x)Molecule(x) ∧ not NotHydroCarbon(x)→ HydroCarbon(x)
C C
CC
Is cyclobutane ahydrocarbon? 3
11
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)→ NotHydroCarbon(x)Molecule(x) ∧ not NotHydroCarbon(x)→ HydroCarbon(x)
C C
CC
Is cyclobutane ahydrocarbon? 3
11
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧ HasAtom(x, y) ∧ not Carbon(y) ∧ not Hydrogen(y)→ NotHydroCarbon(x)Molecule(x) ∧ not NotHydroCarbon(x)→ HydroCarbon(x)
C C
CC
Is cyclobutane ahydrocarbon? 3
11
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧∧
1≤i≤4
HasAtom(x, yi) ∧∧
1≤i≤3
Bond(yi, yi+1) ∧
Bond(y4, y1)∧
1≤i<j≤4
not yi = yj
→ MoleculeWith4MemberedRing(x)
C C
CC
Does cyclobutane contain afour-membered ring? 3
12
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧∧
1≤i≤4
HasAtom(x, yi) ∧∧
1≤i≤3
Bond(yi, yi+1) ∧
Bond(y4, y1)∧
1≤i<j≤4
not yi = yj
→ MoleculeWith4MemberedRing(x)
C C
CC
Does cyclobutane contain afour-membered ring? 3
12
CLASSIFYING OBJECTS
EXAMPLE
Molecule(x) ∧∧
1≤i≤4
HasAtom(x, yi) ∧∧
1≤i≤3
Bond(yi, yi+1) ∧
Bond(y4, y1)∧
1≤i<j≤4
not yi = yj
→ MoleculeWith4MemberedRing(x)
C C
CC
Does cyclobutane contain afour-membered ring? 3
12
UNDECIDABILITY
Logic programs with function symbols can axiomatiseinfinitely large structures
Reasoning with DGLP ontologies is trivially undecidableWe are only interested in finite structures
13
UNDECIDABILITY
Logic programs with function symbols can axiomatiseinfinitely large structuresReasoning with DGLP ontologies is trivially undecidable
We are only interested in finite structures
13
UNDECIDABILITY
Logic programs with function symbols can axiomatiseinfinitely large structuresReasoning with DGLP ontologies is trivially undecidableWe are only interested in finite structures
13
UNDECIDABILITY
Logic programs with function symbols can axiomatiseinfinitely large structuresReasoning with DGLP ontologies is trivially undecidableWe are only interested in finite structures
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
13
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidable
Problem extensively studied in theory of databasesVarious 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidableProblem extensively studied in theory of databases
Various syntax-based acyclicity conditionsweak 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidableProblem extensively studied in theory of databasesVarious 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidableProblem extensively studied in theory of databasesVarious 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidableProblem extensively studied in theory of databasesVarious 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SYNTACTIC ACYCLICITY CONDITIONS
Chase [Maier et al., 1979] termination is undecidableProblem extensively studied in theory of databasesVarious 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
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
14
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
EXAMPLE
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
AceticAcid ≺ Carboxyl
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= Cycle
DGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
SEMANTIC ACYCLICITY
1 Transitive and irreflexive graph ordering which specifieswhich graph instances may imply the existence of othergraph instances
2 Extend the logic program with rules that detect violation ofthe graph ordering
3 Repetitive construction of graph instances during reasoningtriggers derivation of Cycle
A DGLP ontology O is semantically acyclic if O 6|= CycleDGLP ontology with acetic acid is semantically acyclic 3
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
15
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies
2 Decidability of semantic acyclicity for negation-free DGLPontologies
3 Decidability of semantic acyclicity for DGLP ontologies withstratified negation
Semantically acyclic DGLP ontologies with stratifiednegation 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
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies2 Decidability of semantic acyclicity for negation-free DGLP
ontologies
3 Decidability of semantic acyclicity for DGLP ontologies withstratified negation
Semantically acyclic DGLP ontologies with stratifiednegation 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
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies2 Decidability of semantic acyclicity for negation-free DGLP
ontologies3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratifiednegation 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
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies2 Decidability of semantic acyclicity for negation-free DGLP
ontologies3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratifiednegation 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
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies2 Decidability of semantic acyclicity for negation-free DGLP
ontologies3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratifiednegation 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
TECHNICAL RESULTS
1 Termination guarantee for semantically acyclic ontologies2 Decidability of semantic acyclicity for negation-free DGLP
ontologies3 Decidability of semantic acyclicity for DGLP ontologies with
stratified negation
Semantically acyclic DGLP ontologies with stratifiednegation capture a wide range of chemical classes:
Is dinitrogen inorganic? 3
Does cyclobutane contain a four-membered ring? 3
Is acetylene a hydrocarbon? 3
Does benzaldehyde contain a benzene ring? 3
16
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile format
XSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engine
Chemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 molecules
Results:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclic
Molecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expected
Suite of subsumption tests for largest ontology performed infew minutes
17
EMPIRICAL EVALUATION
Data extracted from ChEBI in Molfile formatXSB logic programming engineChemical classes:
HydrocarbonsInorganic moleculesMolecules with exactly two carbonsMolecules with a four-membered ringMolecules with a benzene
Preliminary evaluation ranging from 10 to 70 moleculesResults:
All DGLP ontologies were found acyclicMolecules classified as expectedSuite of subsumption tests for largest ontology performed infew minutes
17
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:
Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:
Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:
Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:Generalise acyclicity condition for datalog rules withexistentials in the head
Relax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negation
User-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntax
Fully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18
OVERVIEW AND FUTURE DIRECTIONS
1 Expressive and decidable formalism for representation ofstructured objects
2 Novel acyclicity condition for logic programs with restricteduse of function symbols
3 Prototype for the structure-based classification of complexobjects
Future directions:Generalise acyclicity condition for datalog rules withexistentials in the headRelax stratifiability criteria for negationUser-friendly surface syntaxFully-fledged classification system for graph-shaped objects
Thank you for listening. Questions?
18