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OWL 2 is widely used to describe complex objects such as chemical molecules; however, OWL 2 axioms cannot represent `structural' features of chemical entities such as having a ring. A combination of OWL 2, rules and \emph{description graphs} (DGs) has been suggested as a possible solution, but an attempt to apply this formalism in a chemical Semantic Web application has revealed several drawbacks. Based on this experience, we present a radically different approach to modelling complex objects via a novel formalism that we call Description Graph Logic Programs. At the syntactic level, our approach combines DGs, rules, and OWL 2 RL axioms, but we give semantics to our formalism via a translation into logic programs interpreted under stable model semantics. The result is an expressive formalism that is well suited for modelling objects with complex structure, that captures the OWL 2 RL profile, and that thus fits naturally into the Semantic Web landscape. Additionally, we test the practical feasibility of our approach by means of a prototypical implementation which provides encouraging results.
Citation preview
CLASSIFYING CHEMICALS USING DESCRIPTION
GRAPHS AND LOGIC PROGRAMMING
Despoina Magka, Boris Motik and Ian Horrocks
Department of Computer Science, University of Oxford
May 28, 2012
OUTLINE
1 MOTIVATION
2 DGLPS, IMPLEMENTATION AND OVERVIEW
1
MODELLING CHEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds[Villanueva-Rosales & Dumontier, OWLED 2007]Chemical information integration[Konyk et al., DILS, 2008 ]Subsumptions between molecules and chemical classes[Hastings et al., OWLED, 2010]
2
MODELLING CHEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds[Villanueva-Rosales & Dumontier, OWLED 2007]
Chemical information integration[Konyk et al., DILS, 2008 ]Subsumptions between molecules and chemical classes[Hastings et al., OWLED, 2010]
2
MODELLING CHEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds[Villanueva-Rosales & Dumontier, OWLED 2007]Chemical information integration[Konyk et al., DILS, 2008 ]
Subsumptions between molecules and chemical classes[Hastings et al., OWLED, 2010]
2
MODELLING CHEMICALS WITH OWL
OWL used for the representation of molecular structures
Classification of chemical compounds[Villanueva-Rosales & Dumontier, OWLED 2007]Chemical information integration[Konyk et al., DILS, 2008 ]Subsumptions between molecules and chemical classes[Hastings et al., OWLED, 2010]
2
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
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation (e.g. hydrocarbons, inorganic molecules,saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation (e.g. hydrocarbons, inorganic molecules,saturated compounds,. . . )
2 Represent rings with adequate precision
(e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation (e.g. hydrocarbons, inorganic molecules,saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation (e.g. hydrocarbons, inorganic molecules,saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)
Prototypical implementation of a logic-based chemicalclassification software
7
RESULTS OVERVIEW
Key idea:Switch from first-order logic to logic programming semantics
Replace classical negation with negation-as-failure
Double benefit:
1 Encode chemical classes based on the absence ofinformation (e.g. hydrocarbons, inorganic molecules,saturated compounds,. . . )
2 Represent rings with adequate precision (e.g. cycloalkanes,benzene rings,. . . )
Expressive decidable logic-based formalism for modellingstructured entities: Description Graph Logic Programs(DGLPs)Prototypical implementation of a logic-based chemicalclassification software
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
Function symbols allow for schema-level reasoning
10
ENCODING DESCRIPTION GRAPHS
Translate DGs into logic programs with function symbols
EXAMPLE
Function symbols allow for schema-level reasoning
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)
Function symbols allow for schema-level reasoning
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)
Function symbols allow for schema-level reasoning
10
CLASSIFYING CHEMICALS
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 CHEMICALS
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 CHEMICALS
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 CHEMICALS
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 CHEMICALS
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 CHEMICALS
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
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
Various syntax-based acyclicity conditions
weak acyclicity [Fagin et al., ICDT, 2002]super-weak acyclicity [Marnette, PODS, 2009]joint acyclicity [Krötzsch and Rudolph, IJCAI, 2011]rule out naturally-arising nested structures
EXAMPLE
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
1AceticAcid
2Methyl
3Carboxyl
1Carboxyl
2Carbonyl
3Hydroxyl
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity condition
checks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the fly
modelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
ACYCLICITY CONDITIONS
Formalisms extensively studied, e.g. Datalog±
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
Novel semantic acyclicity conditionchecks for generation of unbounded structures on the flymodelling of molecules that contain functional groups
Methyl
Carboxyl
Carbonyl
Hydroxyl
O
C
CH3 OH
14
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
15
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
15
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
15
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
15
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
15
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
15
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
15
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
15
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
15
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 automated classification of chemicals
Is dinitrogen inorganic?Does cyclobutane contain a four-membered ring?Is acetylene a hydrocarbon?Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicals
Is dinitrogen inorganic?Does cyclobutane contain a four-membered ring?Is acetylene a hydrocarbon?Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicals
Is dinitrogen inorganic?Does cyclobutane contain a four-membered ring?Is acetylene a hydrocarbon?Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic?Does cyclobutane contain a four-membered ring?Is acetylene a hydrocarbon?Does benzaldehyde contain a benzene ring?
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:
Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:Datalog rules with existentials in the head
User-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:Datalog rules with existentials in the headUser-friendly surface syntax
Fully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16
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 automated classification of chemicalsIs dinitrogen inorganic? 3Does cyclobutane contain a four-membered ring? 3Is acetylene a hydrocarbon? 3Does benzaldehyde contain a benzene ring? 3
Future directions:Datalog rules with existentials in the headUser-friendly surface syntaxFully-fledged chemical classification system
Thank you for listening. Questions?
16