Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies

Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies

A. Patrice Seyed and Stuart C. Shapiro

Department of Computer ScienceCenter for Cognitive Science

University at BuffaloICBO

Introduction

• OBO Foundry Ontologies• Basic Formal Ontology (BFO) as the upper ontology• OBO includes Ratified/Candidate ontologies• But no formal (logical) criteria for ratification• OntoClean– Approach for detecting when the taxonomic relation is

being used improperly• Formal integration between OntoClean’s notion of

Rigidity and BFO’s theory of types

Hypothesis

1. BFO and OntoClean’s notion of Rigidity can be integrated.

2. This integration can serve as a basis for a system that will assist a modeler in alignment with BFO and result in fewer modeler mistakes.

• Provides a modeler with: – Formal System– Decision Tree

BFO

• Restricted set of highly generalized classes• Independent Continuant: Concrete ``Things’’• Dependent Continuant: Qualities, Functions, Roles• Occurrent: Processes

• BFO Classes are types (universals)– Domain level classes are assigned as subclasses

• Restricted set of relations • Disadvantage– Its not always clear how to perform the

assignments

OntoClean• Constraints on taxonomic hierarchies• Rigidity, Identity, Unity, Dependence– Requires a modeler to assign certain features to each

property of an ontology• A property is:

Rigid if it is essential to all instancesNon-Rigid if non-essential to some instanceAnti-Rigid if non-essential to all instances

Constraint: An Anti-Rigid property has only Anti-Rigid subproperties.

Modeling Example Applying Rigidity

• Modeling ExampleIs Compound and Compound Reactant :

Rigid, Non-Rigid, or Anti-Rigid?

Compound

Compound Reactant

Compound Reactant

Compound

Step One: Categorical Unit• BFO– Type (Universal)• What the general terms of science refer to• Person, Student Role, Porous Quality

• OntoClean– Property (attributive)• Meaning of general terms• (being a) Person, (being a) Student, (being) Porous

• Unify Property and Type under the unit of Class

Formal Theory of Classes• subclass_of(A,B) =def "xt(member_of(x,A,t) →

member_of(x,B,t))• exists_at(x,t)– Under a certain ontological theory, object x is within

its domain and x’s existence spans some time, t. • Everything in the domain exists at some time: ∀x∃t(exists_at(x,t)) • membership at a time does not presuppose that

existence spans that time ¬∀xt(∃A member_of(x,A,t)) → exists_at(x,t))

Formal Theory of Classes

• Two Features of classes:

Instantiated(A) =def ∃xt(member_of(x,A,t) ∧ exists_at(x,t)) Members_Exist(A) =def

∀xt(member_of(x,A,t) → exists_at(x,t))

Integrating Rigidity with BFO theory of types

• ``Essential’’ reformulated w.r.t. to time:– Rigid(A) =def "x($t(member_of(x,A,t)) → "t(exists at(x,t) → member_of(x,A,t)))

– Non-Rigid(A) =def $x($t(member_of(x,A,t)) ∧ $t(exists at(x,t) → Ømember_of(x,A,t)))

• Anti-Rigid is incompatible with BFO


• Additional constraints on Rigid, and also on types:– Instantiated– Members_Exist

• "A(Type(A) →

Rigid(A) ∧ Instantiated(A) ∧ Members_Exist(A))


instance_of(x,A,t) =def member_of(x,A,t) ∧ Type(A)

isa(A,B) =def "xt(instance_of(x,A,t) → instance_of(x,B,t))

"AB(isa(A,B) → Type(A) ∧ Type(B))

⊦"A(Non-Rigid(A) → "B(¬isa(A,B) ¬∧ isa(B,A)))

Integration with BFO theory of Types

• We lose the Anti-Rigid constraint.• What have we gained?– Non-Rigid Classes are not Types!?

? Compound

Compound

isa isa

Compound Reactant

Compound Reactant

Modeling Example

molecule-1

molecule-2 molecule-3

molecule-4

molecule-1


molecule-4

compound-1

compound-2 compound-3

???

compound-1


compound-4reactantRole-1

reactantRole-2 reactantRole-3

Compound

isa

Compound Reactant

Modeling Example

molecule-1


molecule-4

molecule-1


molecule-4

compound-1


Compound Reactant-Role

compound-1


compound-4reactantRole-1


Compound

Role_Of

subclass_ofCompound Reactant

Modeling Example

Compound Reactant

molecule-1


molecule-4


compound-1


compound-4

compound-1


reactantRole-1


Compound

Role_Of

Has_Rolesubclass_of

Compound Reactant

molecule-1


molecule-4


compound-1


compound-4

compound-1


reactantRole-1


Compound

Role_Of

Has_Role

Independent Continuant Dependent Continuant

compound-2 compound-4 compound-3 compound-1

reactantRole-1 reactantRole-2 reactantRole-3

subclass_of

isa isa

Modeling Example

Compound Reactant

molecule-1


molecule-4

Role

compound-1


compound-4

compound-1


?

? ?

Compound

subclass_of???

Decision Tree

• Proactive Avoidance of Multiple Inheritance and enforces examination of Non-Rigid classes– Introduces a class, one at a time– Asks a modeler to supply an example member of the

class– Yes/No Questions

• Correspond Upper Level Divisions, BFO/Rigidity Integration, Type-Level relations

• A gentle approach of linking to BFO classes, and a refactoring when Non-Rigid classes are identified

Role_Of

Compound Compound Reactant-Role

Entity

Has_Role

Independent Continuant Dependent Continuant

Compound Reactant

isa isa

isa isa

subclass_of

Integration Summary

• Class covers both OntoClean’s notion of property and BFO’s notion of type.

• A class might or might not satisfy Instantiated, Members_Exist, Rigid, or Non-Rigid– the latter two capturing the intuitions of Rigidity

within our formal theory • BFO’s notion of type is captured by a class that

satisfies Instantiated, Members_Exist, and Rigid.

Future Work

• Rigidity and Canonical domains• Connection of Non-Rigidity and Other Type-

Level Relations• Expert review of decision tree procedure– Evaluate “accessibility” of questions

• Integrate other OntoClean Components

Documents

Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies