Classifying Chemicals with Description Graphs and Logic Programming

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